Arts, Faculty of
Linguistics, Department of
DSpace
UBCV
Khalaji Pirbaluti, Zara
Master of Arts - MA
University of British Columbia
Morpho-phonological phenomena present challenges to learners because they interface with morpho-syntactic, semantic, and phonological grammar. A common difficulty encountered in these interface phenomena lies in navigating idiosyncrasies and exceptional cases. This thesis explores the nature of learning implications of morpho-phonological alternations, in particular focusing on the case study of patterns akin to French liaison. Liaison is a prevalent and complex phenomenon in French that occurs at word boundaries. I propose a theoretical account of the learnability of French liaison within the Optimality Theory framework which gives rise to predictions regarding various components and dimensions of learning. I evaluate these predictions in an experimental study with an artificial language learning paradigm that consists of a training phase and a testing phase with two-alternative-forced-choice tasks. The training phase has a between-subject design where learners experience different hypothesized learning trajectories. The aim of the experiment is to investigate the extent to which learners would face challenges in learning given that the artificial language includes idiosyncratic patterns. The results demonstrate that in a controlled experimental setting, adult learners do show partial differential learning outcomes depending on their learning trajectory in training. However, participants also show task-dependent performance: above-chance for noun phrase choices but near-chance for word segmentation with both novel and familiar nouns. These results, taken together, imply that one of the most challenging components of learning in patterns similar to liaison predominantly lies in mechanisms related to computing word boundaries and deriving representations.
LEARNING MORPHO-PHONOLOGICAL ALTERNATIONS LIKE FRENCH LIAISON: AN ARTIFICIAL LANGUAGE LEARNING STUDY by Zara Khalaji Pirbaluti A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Linguistics) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2025 © Zara Khalaji Pirbaluti, 2025 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled: Learning morpho-phonological alternations like French liaison: an artificial language learning study submitted by Zara Khalaji Pirbaluti in partial fulfilment of the requirements for the degree of Master of Arts in Linguistics Examining Committee: Anne-Michelle Tessier, Associate Professor, Linguistics, UBC Supervisor Gunnar Ó. Hansson, Associate Professor, Linguistics, UBC Supervisory Committee Member Carla L. Hudson Kam, Professor, Linguistics, UBC Supervisory Committee Member iii Abstract Morpho-phonological phenomena present challenges to learners because they interface with morpho-syntactic, semantic, and phonological grammar. A common difficulty encountered in these interface phenomena lies in navigating idiosyncrasies and exceptional cases. This thesis explores the nature of learning implications of morpho-phonological alternations, in particular focusing on the case study of patterns akin to French liaison. Liaison is a prevalent and complex phenomenon in French that occurs at word boundaries. I propose a theoretical account of the learnability of French liaison within the Optimality Theory framework which gives rise to predictions regarding various components and dimensions of learning. I evaluate these predictions in an experimental study with an artificial language learning paradigm that consists of a training phase and a testing phase with two-alternative-forced-choice tasks. The training phase has a between-subject design where learners experience different hypothesized learning trajectories. The aim of the experiment is to investigate the extent to which learners would face challenges in learning given that the artificial language includes idiosyncratic patterns. The results demonstrate that in a controlled experimental setting, adult learners do show partial differential learning outcomes depending on their learning trajectory in training. However, participants also show task-dependent performance: above-chance for noun phrase choices but near-chance for word segmentation with both novel and familiar nouns. These results, taken together, imply that one of the most challenging components of learning in patterns similar to liaison predominantly lies in mechanisms related to computing word boundaries and deriving representations. iv Lay Summary The goal of this thesis is to improve our understanding of how certain sound patterns are learned when they are exceptions to the general sound patterns in a language. My study focuses on one system of sound patterns in French as its unique characteristics presents various challenges for language acquisition. In French, certain arbitrary words, like petite meaning ‘small’, have two forms in pronunciation, and the choice between forms depends on whether the following noun starts with a vowel or a consonant. In this thesis, I create an artificial mini-language using nonsense words that mimic the sound patterns of French and present it to adult participants in an online experimental study. The participant errors are similar to children and show that they struggle learning the nouns starting with a vowel. However, they can judge which pattern is correct when they get the full phrase. v Preface This thesis is original and independent work by the author. The experiment and associated methods were approved by the University of British Columbia’s Behavioral Research Ethics Board (#H23-02492). No Generative Artificial Intelligence tools were used in the research process, development, or writing of the thesis. Portions of the text related to the experiment and the discussion have been submitted for publication in the proceedings of the 2024 ACL/CLA conference, as Khalaji Pirbaluti and Tessier (to appear). I was the lead investigator for this project, responsible for all major areas of concept formation, experimental design, stimulus preparation, data collection and analysis, as well as manuscript composition. Anne-Michelle Tessier was also involved in concept formation and experimental design. Khalaji Pirbaluti, Z. and Tessier, A.-M. (to appear). Artificial morpho-phonological learning: a study based on French liaison. In Bembridge, G., editors, Proceedings of the 2024 meeting of the annual conference of the Canadian Linguistic Association. vi Table of contents Abstract _____________________________________________________________________ iii Lay Summary ________________________________________________________________ iv Preface______________________________________________________________________ v Table of contents ______________________________________________________________ vi List of Tables _______________________________________________________________ viii List of Figures ________________________________________________________________ ix Acknowledgements ____________________________________________________________ xi Dedication __________________________________________________________________ xiii 1. Introduction ____________________________________________________________ 1 1.1. General overview _____________________________________________________ 1 1.2. Scope and significance of the study _______________________________________ 2 2. Background and Theoretical Framework _____________________________________ 4 2.1. Introduction to phonologically conditioned allomorphy _______________________ 4 2.2. French liaison ________________________________________________________ 5 2.3. Developmental path of morpho-phonological acquisition and the literature on child acquisition of liaison __________________________________________________ 7 2.4. Learnability of liaison as a morpheme-specific phonological phenomenon within Optimality Theory ___________________________________________________ 12 2.4.1. Learning the underlying representation _______________________________ 14 2.4.2. Initial state grammar to end state grammar _____________________________ 17 2.5. Predictions of the learning theory in the current study _______________________ 28 2.5.1. Ordered learning trajectory - Liaison first _____________________________ 29 2.5.2. Ordered learning trajectory - Non-liaison first __________________________ 33 2.5.3. Mixed Learning trajectory _________________________________________ 35 2.5.4. Predicted outcomes of trajectories ___________________________________ 40 3. Methods______________________________________________________________ 47 3.1. Participants _________________________________________________________ 47 3.2. Overview of design __________________________________________________ 47 3.3. Materials ___________________________________________________________ 48 3.3.1. Training and testing Stimuli ________________________________________ 48 3.3.2. Audio stimuli ___________________________________________________ 50 vii 3.3.3. Visual stimuli ___________________________________________________ 50 3.4. Experimental procedure _______________________________________________ 51 3.4.1. Training ________________________________________________________ 51 3.4.2. Testing_________________________________________________________ 55 3.5. Data collection procedure and data analysis _______________________________ 59 4. Results _______________________________________________________________ 61 4.1. Task1 - Phrase Judgement _____________________________________________ 61 4.2. Task 2 - Familiar Segmentation _________________________________________ 66 4.3. Task 3 - Novel Segmentation ___________________________________________ 70 4.4. Task2 and 3 – Both Segmentation Tasks __________________________________ 74 5. Discussion ____________________________________________________________ 76 5.1. The effect of all the independent variables on learning _______________________ 76 5.2. The effect of the interaction of input data structure and test trial types on learning _ 77 5.2.1. Computing the underlying representation (in alternations) ________________ 78 5.2.2. Reranking stages _________________________________________________ 85 5.2.3. Constraint cloning and lexicon indexation _____________________________ 88 5.3. Pilot experiment and the universal biases in segmentation ____________________ 93 5.4. Analysis of the subset of successful learners _______________________________ 97 5.5. Analysis of the effect of segmentation accuracy on the phrase judgement task ___ 101 5.6. Conclusion and future work ___________________________________________ 103 Bibliography _______________________________________________________________ 106 Appendices ________________________________________________________________ 114 Appendix A. Stimuli lists ___________________________________________________ 114 Appendix B. Statistical summaries ___________________________________________ 119 1. Task1 - Phrase Judgement ______________________________________________ 119 2. Task2 - Familiar segmentation ___________________________________________ 121 3. Task 3 - Novel segmentation ____________________________________________ 122 4. Task 2 and 3 - Both segmentation tasks ____________________________________ 124 5. Analysis of the subset of successful learners ________________________________ 126 6. Analysis of the segmentation accuracy _____________________________________ 127 viii List of Tables Table 2-1. The summary of learning trajectories of the three groups of learners ____________ 42 Table 2-2. The summary of predictions of difficulty of learning by different aspects ________ 45 Table 3-1. Word1 stimuli representing alien names __________________________________ 49 Table 3-2. Word2 stimuli representing everyday object nouns _________________________ 49 Table 3-3. Structure and the content of the blocks in the training phase of the experiment ____ 54 Table 3-4. Pseudo-randomization structure inside each training block ___________________ 55 Table 3-5. The structure of the tasks in the testing phase of the experiment _______________ 56 Table 3-6. Testing trial types in task 1 (phrase judgement) with examples ________________ 57 Table 3-7. Testing trial types in task 2 (familiar segmentation) with examples _____________ 58 Table 3-8. Testing trial types in task 3 (novel segmentation) with examples_______________ 59 Table 4-1. Mean accuracy by condition across trial type in task 1 (phrase judgement) _______ 63 Table 4-2. Pairwise comparisons in the statistical model based on the emmeans package in task 1 (phrase judgement) ___________________________________________________ 65 Table 4-3. Mean accuracy by condition across trial type in task 2 (familiar segmentation) ___ 67 Table 4-4. Pairwise comparisons in the statistical model based on the emmeans package in task 2 (familiar segmentation) _______________________________________________ 69 Table 4-5. Mean accuracy by condition across trial type in task 3 (novel segmentation) _____ 72 Table 4-6. Pairwise comparisons in the statistical model based on the emmeans package in task 3 (novel segmentation) _________________________________________________ 73 Table 5-1. Pseudo-randomization order for Alt1st condition ___________________________ 79 Table 5-2. Predictions and results of learning the underlying representation _______________ 80 Table 5-3. Schema of possible interpretations based on trial types in segmentation tasks ____ 81 Table 5-4. Predicted probabilities (95% CI) in V-initial and C-initial trials in segmentation tasks __________________________________________________________________ 82 Table 5-5. Pseudo-randomization order in the Mixed condition ________________________ 84 Table 5-6. Predictions and results of reranking stages ________________________________ 85 Table 5-7. Average accuracy in the two subtypes of itemNonAlt trials in task 1 (phrase judgement) _________________________________________________________ 87 Table 5-8. Predictions and results of lexical indexation and constraint cloning ____________ 89 Table 5-9. Judgement task - schema of possible interpretations based on trial types ________ 91 Table 5-10. Average accuracy in itemNonAlt and itemAlt trials in the Judgement task ______ 92 Table 5-11. The proportion of the successful learners to all participants __________________ 98 ix List of Figures Figure 2-1. Interdependence of the three factors of output, underlying representation and constraint hierarchy in language acquisition taken from Kager (2004:323) ______ 12 Figure 2-2. Partition in the phonological grammar related to word1s in liaison or non-liaison classes____________________________________________________________ 13 Figure 3-1. Step-by-step overview of the experimental design _________________________ 48 Figure 3-2. Visual stimuli used for word1 and a sample of visual stimuli used for word2 ____ 51 Figure 3-3. A sample page of all experimental trials in the web browser _________________ 52 Figure 4-1. Overall accuracy by condition in task 1 (phrase judgement) __________________ 62 Figure 4-2. Accuracy by condition across trial type in task 1 (phrase judgement) __________ 63 Figure 4-3. Mean accuracy by condition across item familiarity in task 1 (phrase judgement) _ 64 Figure 4-4. Predicted probabilities of correct responses for each combination of condition and trial type in task 1 (phrase judgement) ___________________________________ 66 Figure 4-5. Overall accuracy by condition in task 2 (familiar segmentation) ______________ 67 Figure 4-6. Accuracy by condition across trial type in task 2 (familiar segmentation) _______ 68 Figure 4-7. Mean accuracy by condition across item familiarity in task 2 (familiar segmentation) _________________________________________________________________ 68 Figure 4-8. Predicted probabilities of correct responses for each combination of condition and trial type in task 2 (familiar segmentation) _______________________________ 70 Figure 4-9. Overall accuracy by condition in task 3 (novel segmentation) ________________ 71 Figure 4-10. Accuracy by condition across trial type in task 3 (novel segmentation) ________ 72 Figure 4-11. Predicted probabilities of correct responses for each combination of condition and trial type in task 3 (novel segmentation) _________________________________ 74 Figure 4-12. Predicted probabilities of correct responses for each combination of condition and trial type in task 2 and 3 (segmentations) ________________________________ 75 Figure 5-1. Pilot vs current experiment - Mean accuracy by condition in the familiar segmentation task ___________________________________________________ 95 Figure 5-2. Pilot vs current experiment - Mean accuracy by condition in the novel segmentation task ______________________________________________________________ 96 Figure 5-3. Subset of the successful learners vs. all learners in task 1 (phrase judgement) ____ 99 Figure 5-4. Subset of the successful learners vs. all learners in task 2 (familiar segmentation) 100 Figure 5-5. Subset of the successful learners vs. all learners in task 3 (novel segmentation) _ 101 Figure 5-6. Predicted probabilities of a correct response in the judgement task by accuracy score in segmentation across trial types _____________________________________ 102 x Figure 5-7. Predicted probabilities of a correct response in the judgement task by accuracy score in segmentation across conditions _____________________________________ 103 xi Acknowledgements I could not have accomplished writing this thesis, had it not been for the help and support of many people. To begin, I hope what follows serves as the most direct way to convey my sincerest sentiments, even if after hours wrestling with words, they are still not the most original phrasing and lean towards cliché. First and foremost, I would like to thank my supervisory committee, Anne-Michelle Tessier, Gunnar Hansson, and Carla Hudson Kam for their unwavering support and guidance. Words cannot express my gratitude towards my supervisor, Anne-Michelle Tessier. Her invaluable timely feedback and illuminating insights were the driving force behind this work. Her wisdom on the art of being concise, and conveying only what is sufficient and necessary is a lesson I will never forget. Our weekly meetings were filled with instances of her patiently transforming the essence of what I hoped to say into clear ideas from what usually resembled a heap of long rigmarole (probably my brain's optimal output form) and then guiding me to improve my arguments and nail them down concisely in writing. Her intellectual passion and influence undoubtedly will always be what inspires my curiosity to seek answers to questions surrounding our understanding of phonological acquisition far beyond this thesis. I truly appreciate how fortunate I am to have had the presence of her and my supervisory committee in my academic journey. Their encouragement has been a beacon pushing me forward to reach new heights I did not think I could, yet simultaneously gently nudging me to stay grounded in the bigger picture. They made it possible to stay on track and achieve tasks on time whenever I lunched myself in multiple directions self-indulgently focusing on tiny corners of problems at hand. I owe so much of what I know about developmental findings in language acquisition to Carla Hudson Kam who shared her knowledge and experience with genuine willingness, and openness. Her emphasis on methodological detail, reader-oriented writing, and the importance of developing well-thought-out experimental design in our meetings were instrumental in the completion of this thesis and my growth as a researcher. Gunnar Hansson’s sharpness at detecting where the logic falls apart and his patience in explaining the role of a crucial detail or fundamental assumptions in my analyses never ceased to fill me with awe. It is no surprise how I always walked out of our meetings invigorated with so much food for thought. I would be remiss if I did not mention his comments were paramount in improving the quality of drafts of this thesis until the finishing line. It goes without saying that all the errors and shortcomings are my own. One of the most rewarding aspects of my time at UBC was the opportunity to learn from and work under remarkable faculty members who exemplify what it means to be an impactful teacher and a rigorous scholar: Douglas Pulleyblank, Rose-Marie Déchaine, Lisa Matthewson, Henry Davis, Hotze Rullmann, Molly Babel, Kathleen Hall and Márton Sóskuthy. Not only their approach to pedagogy, scientific inquiry, and problem-solving will leave a long-lasting impression xii on me, but also their dedication, boundless passion, and selflessness toward the field, students, and communities are an unlimited source of inspiration. I am also indebted to Golnaz Modarresi Ghavami who despite being more of a phonetician managed to turn me onto phonology by showing me how fascinating it can be. Merci, Ostad. I benefited greatly from companionship and intellectual discussion with all my fellow graduate students. I extend my heartfelt thanks to all of them for their friendship and great memories, while only having the space to acknowledge a subset: Alex Ayala, Kaili Vesik, Sijia Zhang, Gloria Mellesmoen, Oksana Tkachman, Emily Sadlier-Brown (who all beta-tested the experiment and offered me feedback during my lengthy presentations at the Child Phonology and Language & Learning labs), Anna Stacey, Line Lloy, Ella Hannon, Reed Steiner, Ariwan Addy Suhairi, Starr Sandoval, Noah Luntzlara, Ana Arrieta Zamudio, Michelle Kamigaki-Baron, Suyuan Liu, Brian Diep, Bruce Oliver, Rose Underhill, Roger Lo, and Michael Schwan. Alex deserves a massive thank you, she generously agreed to spare her time to help with the recording of the audio stimuli and was a constant source of encouragement and a perceptive listener when I was stuck in various stages. I owe a great deal of thanks to my parents and my family for nurturing me and feeding me learning data to transform my UG into at least one fully-fledged language enabling me to form complex thoughts so hopefully I would be able to externalize them and communicate with other humans. They are not to blame for any lack of clarity in my communication and writing style, though, as that is my responsibility for not practicing enough after the critical period. Despite never questioning my ambitions, my parents have often clear signs of boredom on their faces when I start to ramble on about my research and how my experiments keep running into roadblocks, which is completely unforgivable given that they were the ones who instilled in me a profound love for science and education from a young age. All in all, it would not have been possible for me to be at liberty to dedicate most of my adult life so far to what I love and enjoy the most without their sacrifices and unconditional, unequivocal support. Truthfully, I do not know how to thank them adequately. Lastly, I also would like to give a huge shoutout to the Whitecaps for providing me with my much-needed evening weekly dose of the beautiful ol’ game which was like a lifeline during grad school—just as essential for survival as catching enough sleep. Up the 'caps! ∞ Finally, I point out that this thesis was supported in part by an SSHRC Insight Grant #435-2023-0169 titled “Learning French liaison: the roles of input, grammar and frequency” awarded to Anne-Michelle Tessier. xiii Dedication To spreadsheets, “When trouble’s near and doubt’s about, Run in circles, let it all out, Then make a spreadsheet, without a doubt— You’ll feel better, sorted out!” 1 Chapter 1 Introduction 1. Introduction 1.1. General overview Phonologically conditioned allomorphy is a cross-linguistically common interface phenomenon that invokes the knowledge of different modules of the grammar (morphology, syntax, and phonology). Despite receiving great attention in the theoretical morpho-phonological literature (for overviews see Nevins, 2011; Wolf, 2008; Paster, 2006) and a series of experimental studies using wug tests and similar methodology within the child acquisition literature (Finn and Hudson Kam, (2015), Zamuner et al., 2012. Kerkhoff, 2007, Berko, 1958), experimental studies that focus on the learning of phonologically conditioned allomorphy patterns and exceptions are not numerous (cf. Finley, 2023, 2021, Baer-Henney et al., 2015; Coetzee, 2009). The main goal of this thesis was to provide some insights regarding phonological alternation patterns which are idiosyncratic and not language-wide from a learnability perspective. The specific case study that was the focus of this thesis is a morpho-phonological pattern in French called liaison (Côté, 2011; Tranel, 1995a; Morrison, 1968). Liaison is a prevalent yet idiosyncratic external sandhi phenomenon that occurs at the boundary of two words in various configurations. The specific morpho-syntactic configuration of liaison which this study concentrates on is the nominal domain, for instance the adjective + noun configurations (e.g., [pətit]/[pəti]: petit ours [pə.ti.tuʁs] ‘little bear’ vs. petit prince [pə.ti.pʁɛs̃] ‘little prince’). The alternations of the first word are phonologically conditioned by the following word’s V- or C-initial segment, similar to the conditions of the indefinite determiner allomorphy in English a/an. However, the liaison pattern in French involves some idiosyncrasies that challenge the learner. In contrast to English, the set of morphemes with the same allomorphy pattern not only includes the indefinite determiner but also several other functional and non-functional morphemes. Nevertheless, the pattern does not become fully regular or language-wide as many counterexamples are found (e.g. in adjective + noun configuration, [ʒœn]: jeune ours [ʒœ.nuʁs] ‘young bear’ vs. jeune prince [ʒœn.pʁɛs̃] ‘young prince’). 2 By choosing this case study, the objective was to explore the implications of theories of learning for idiosyncratic patterns. For this purpose, I adopted the constraint indexation model in Optimality Theory (Pater, 2010) as the basis for the learning-based theoretical framework and designed an artificial language learning experiment to evaluate the predictions generated by that account. It is important to note that several alternative theoretical approaches exist in the literature for capturing similar morpho-phonological alternations. These include co-phonologies (Inkelas and Zoll, 2007; Ito and Mester, 1995) for addressing morpheme-specificity, gradient symbolic representations (Smolensky and Goldrick, 2016) concerning the unique status of certain representations, and Distributed Morphology (Embick, 2010) to explain allomorph selection. However, the nature of the constraint indexation model more readily allows for comparisons of predictions across learners within an experimental framework. 1.2. Scope and significance of the study This thesis aims to empirically investigate the challenging aspects of learning emerging from the patterns in the learning data with regard to a pre-nominal idiosyncratic external sandhi phenomenon like French liaison. In liaison, there are two main learning challenges. The classification of morphemes in the lexicon that do or do not participate in liaison is not based on phonological surface information and is considered to be phonologically arbitrary1. In addition, in the context of noun phrases, the prenominal location of liaison is significant for learning the lexicon, as well as learning the phonological grammar which presents a unique challenge from a learnability perspective. By examining an edge case like liaison in French, the findings of this study may have broader implications for learning theories as a whole. Even though liaison-like patterns are rare, similar challenging patterns are also found in cases such as the initial consonant mutation in Celtic languages (Hannahs, 2011), and voicing alternation in Japanese Rendaku (Rosen, 2003). To tackle a learnability question, a thorough investigation of the interaction of errors occurring during acquisition and trajectories of learners necessitates longitudinal studies that often face substantial logistical and design difficulties. Artificial Language Learning (ALL) paradigms are an alternative method among the experimental studies in the literature that have been successful in examining the impact of biases and challenges in learning (Culbertson, 2024; Finley, 2023; Glewwe, 2022; Chong, 2021; Linzen and Gallagher, 2017; Hayes and White, 2013; Moreton and 1 In some theoretical accounts (such as in non-linear phonology), differences in phonological representations are used to explain the distinction between liaison vs non-liaison word1s (e.g., Tranel, 1995b). However, from the perspective of a theory of learnability in this thesis, this is a phonologically arbitrary classification that is achieved with non-phonological indexation. 3 Pater, 2012a, 2012b; Tessier 2012 among others). An experimental study that artificially simulates a learning scenario could have implications for theories of learnability. If certain dimensions of learning are not as challenging as the rest, relevant mechanisms and components entailed in theories of learnability could be modified to better capture how learning is achieved by learners. Therefore, this thesis benefits from an Artificial Language learning paradigm. These experiments can take a variety of forms and designs, but often they are designed in two phases: a. training phase where participants are trained by being exposed to learning data using audio, text, or visual stimuli; b. testing phase where participants are tested on data exactly matching the training data and/or additional novel data (depending on the design) by performing tasks. In the current experiment, incorporating a typical artificial language learning paradigm, the learning scenario was as similar as possible to language acquisition by children. The experiment’s training phase provided an opportunity for implicit learning where there is no negative learning data or feedback. However, as opposed to real life acquisition, it is possible to control for semantic information. I designed three training conditions for three groups of learners: either to begin with the class of morphemes that participate in liaison or the class of morphemes that do not, or to receive both classes at the same time. Importantly, the training condition trajectories differ in the order in which the learning data unfolds, not any other aspect such as the frequency or amount of the data. Focusing on the distribution and order of learning data throughout the experimental training, the objective of testing is to investigate whether there is a differential learning outcome depending on the difficulty level emerging from the training conditions. The results do not fully align with predictions regarding the challenging aspects of learning; however, they indicate that learners’ accuracy could to some extent be predicted by the training conditions. Overall, the difficulty level of the tasks and inter-participant variation, in addition to stronger universal biases against language-specific segmentation preclude observing a statistically significant interaction between the types of errors and different training conditions, and further research is needed to be able to clarify the impact of the distribution and order of learning data for patterns such as liaison. However, one of the implications that stem from the results of the current study may be that the most challenging component of learning predominantly lies in mechanisms related to computing boundaries and selecting representations. The structure of this thesis is as follows: In Chapter 2, I present an analysis grounded in an Optimality theoretic framework that addresses the learnability issues discussed followed by predictions and research questions building on the learnability theory. Chapter 3 discusses the methodology and details of the experiment design. The results of the experiment and the accompanying statistical analyses are detailed in Chapter 4. The thesis ends with a discussion of the implications concerning the research questions and conclusion in Chapter 5. 4 Chapter 2 Background and Theoretical Framework 2. Background and Theoretical Framework 2.1. Introduction to phonologically conditioned allomorphy Allomorphy refers to the variations in a morpheme’s phonological form, often controlled by contextual linguistic factors arising from morpho-syntax or morpho-phonology. The allomorph variants of a morpheme can exhibit various degrees of phonological dissimilarity and idiosyncrasy. For example, the verb to be in English presents three dissimilar forms in the present tense (am/is/are) that are morphologically conditioned and somewhat idiosyncratic, as the choices are not consistent across person and number. In contrast, the two indefinite article forms in English (a/an) are more phonologically similar and demonstrate regular conditioning, as the choice depends on whether the noun begins with a vowel or consonant. The latter example is commonly referred to as phonologically conditioned allomorphy (PCA), where the phonological context determines the selection of the allomorph. In such cases, the allomorphs selected can often be considered as optimizing and motivated by avoiding marked phonological structure (cf. “non-optimizing phonologically conditioned suppletive allomorphy” in Paster, 2006: 76-97). Nevins (2011) outlines six types of phonological conditions that lead to optimized and natural outputs. The most prevalent type involves conditions that produce optimized (unmarked) syllable structures, ranging from preference for onsets, dispreference for codas, or sonority drops in codas (for a comprehensive review, see Nevins, 2011: 6-8; Paster, 2006: 63-71). Besides at the level of syllable structure, other types of phonological conditions can appear at the level of segments or prosody. The next section will introduce the case study focusing on a phonologically conditioned allomorphy phenomenon in French. French liaison presents challenges regarding the phonological conditions governing allomorph selection and representations which will have consequences for learning. 5 2.2. French liaison Liaison is a frequent and widespread morpho-phonological phenomenon in French which has received great attention over the years in the study of the phonological grammar of French (Storme, 2024; Smolensky and Goldrick, 2016; Tranel, 2000; Selkirk, 1974). In terms of its domain, it is categorized as external allomorphy where the conditioning factors are determined by phonological information in adjacent words in the higher prosodic domain. In this respect, liaison is also known as an external sandhi phenomenon , since the alternation occurs at the boundary of two words. The locus of liaison is limited to certain syntactic configurations; at the same time, it is also affected by variation and sociolinguistic variables (Meinschaefer, Sven and Frisch, 2015; Durand and Lyche, 2008). The following data points illustrate the basic pattern in prenominal configurations. The examples (1−4) are of noun phrases with two syntactic configurations in which liaison applies, including [determiner + noun] and [adjective + noun] such as (1) the plural definite article les with the allomorphs [le]/[lez], (2) the masculine singular indefinite article un with the allomorphs [œ̃]/[œ̃n], (3) the numeral modifier deux ‘two’ with [dø]/[døz] and (4) the masculine singular adjective petit ‘little’ with [pəti]/[pətit]: (1) (2) a. les bébés [le.be.be] ‘the babies’ a. un bébé [œ̃.be.be] ‘a baby’ b. les amis [le.za.mi] ‘the friends’ b. un ami [œ̃.na.mi] ‘a friend’ c. les ours [le.zu.ʁs] ‘the bears’ c. un ours [œ̃.nuʁs] ‘a bear’ (3) (4) a. deux bébés [dø.be.be] ‘two babies’ a. petit bébé [pə.ti.be.be] ‘little baby’ b. deux amis [dø.za.mi] ‘two friends’ b. petit ami [pə.ti.ta.mi] ‘little friend’ c. deux ours [dø.zuʁs] ‘two bears’ c. petit ours [pə.ti.tuʁs] ‘little bear’ The final consonant, here [z, n, t] in bold, in the VC# allomorphs is referred to as the “liaison consonant” (LC) in the literature. The basic generalization in these examples is that some structural property of the following words determine the presence of the allomorph containing the liaison consonant or lack thereof. As examples (a-c) for each allomorph set show, the onset of the left word (nouns) seems to be conditioning the choice of the allomorph in the right morpheme. Examples (a) are C-initial nouns, resulting in the selection of the V-final allomorph. In contrast, examples (b) and (c) demonstrate V-initial nouns, which results in the allomorph containing the liaison consonant. To fully understand the role of this pattern in the morpho-phonological system of French, it is essential to recognize that morphemes with allomorph pairs, that is those involved in liaison, are lexically determined and do not constitute a coherent class. According to Côté (2011: 5) the 6 morphemes grouped under liaison are argued to be either among closed lexical classes or specific morphological categories. The determiners (1−2) are an example of the closed class of morphemes, other functional morphemes in this category are clitics, conjunctions, and prepositions. The specific morphological categories include adjectives, nouns, adverbs, within compounds and fixed phrases. However, it is crucial to note that this is not a language-wide pattern; for instance, not all [adjective + noun] configurations in French follow the same pattern across-the-board. The data in (5) shows two masculine adjectives which do not undergo liaison. Examples (5a) and (5b) show C-initial nouns and examples (5c) and (5d) V-initial nouns which all co-occur with non-alternating adjectives joli [ʒɔli] and jeune [ʒœn]. (5) a. joli bébé [ʒɔli.be.be] ‘pretty baby’ b. jeune bébé [ʒœn.be.be] ‘young baby’ c. joli ami [ʒɔli.a.mi] ‘pretty friend’ d. jeune ami [ʒœ.na.mi] ‘young friend’ The contrast in examples (4 vs. 5) illustrate an important empirical pattern to be captured, whereby a situation is created for phonological processes favouring naturally well-formed structures in an allomorph to be restricted to only certain morphemes. The nature of these restrictions appears quite arbitrary which even seems to be insensitive to the morpho-syntactic categories of morphemes. This is evident from the fact that certain groups of prenominal adjectives possess allomorphic pairs (4), while others do not (5). From the point of view of acquisition, it is worth mentioning that the right words also contribute to creating added irregularities in the pattern. Therefore, considering the phenomenon as a whole, idiosyncratic and morpheme-specific characteristics extend to the right words which were introduced as the conditioning factor. Examples in (6) illustrate that certain nouns traditionally categorized as h-aspiré are anticipated to condition the C-final allomorph but in fact resist it (for a review of historical facts see Southworth, 1970). A small group of words such as homard, héros, and hibou which phonologically begin with a vowel in modern French, function as if they are C-initial, thereby not selecting the allomorph containing the liaison consonant (cf. examples b and c in 1−4). Therefore, in the event that a h-aspiré noun constitutes the context in prenominal liaison, the basic generalization does not hold and the regular phonological sensitivity of the plural definite morpheme is neutralized. 7 (6) a. les homards [le.ɔm.aʁ] *[le.zɔm.aʁ] ‘the lobsters’ b. les héros [le.eʁo] *[le.zeʁo] ‘the heroes’ c. les hiboux [le.ibu] *[le.zibu] ‘the owls’ After having examined the basic synchronic patterns and characteristics of morphemes within the higher prosodic domain where liaison occurs, it must be noted that the system of liaison has evolved over hundreds of years (Morin, 2005). The idiosyncratic nature and irregularities observed are largely attributed to diachronic factors. Overall, the irregular interactions between phonological elements and morphology give rise to various analyses and competing theories concerning the organization of grammar. Several accounts have also been proposed about the affiliation of the liaison consonant (for a summary see Côté, 2011: 8; Tessier et al., 2023: 3; Storme, 2024: 31) where it could be associated with the word1 (e.g., les), word2 (e.g., ami), both or neither. This system of liaison, shaped by both synchronic and diachronic influences, has sparked debates regarding the mechanisms of allomorphy selection. Some accounts emphasize morphological listing (Paster, 2006; Embick, 2010), while others such as Smith (2015) advocate for constraint-based models where the ranking of phonological and morphological constraints select the underlying representations. As Nevins (2011: 23) notes, using artificial language acquisition experiments where “diachrony is fully controlled by the experimenter and nonetheless the learner demonstrates the emergence of a preference for phonological optimization based on sparse or insufficient data” can be a good test bed for this debate. In the next section, to shed some light on the extent to which the role of phonology is central in speakers' minds, the literature on children's acquisition of French liaison is reviewed to discuss different approaches explaining empirical results in experimental studies with young children. Additionally, a brief overview of developmental stages in morphophonemic learning is provided. 2.3. Developmental path of morpho-phonological acquisition and the literature on child acquisition of liaison It is generally accepted that early in the developmental path of phonological acquisition infants exhibit signs of developing sensitivity to phonotactic patterns, allowing them to build their foundational phonological knowledge by 8 to 12 months of age (for a recent review, see Sundara et al., 2022; Jusczyk, 2000). Learning about alternations typically occurs later, starting around 12 months (White and Sundara, 2014). Perception studies support this notion, revealing that infants 8 (approximately 9 months old) can distinguish phonotactic probabilities among words (Friederici and Wessels, 1993) and employ this distributional information for word segmentation (Mattys and Jusczyk, 2001), as well as for learning (voicing) alternations (White et al., 2008). A longitudinal study by Luckaszewicz (2006) reports that a child aged 3;5-8 was more successful at mastering alternations that reflect the phonotactic rules of Polish than those found only in specific morphemes. These studies suggest that phonotactic knowledge may play a crucial role in guiding the subsequent learning of alternations. Further along the developmental path, evidence regarding infants' receptive morphological knowledge indicates that they display sensitivity to morpho-phonological patterns in their second year of life, well before they achieve mastery of these patterns in later stages (Soderstrom et al., 2007). Understanding morpho-phonological alternations involves mapping variations in surface forms to underlying representations and recognizing morphemes’ distinct meanings. In this context, the literature on morphological acquisition illustrates that the discovery of meaning influences infants' acquisition of suffixes (Mintz, 2013). However, more recent experiments reveal that children's knowledge of morphology develops concurrently with their understanding of phonology and semantics in English (Kim and Sundara, 2021) as well as in French (Marquis and Shi, 2012). In fact, Kim and Sundara (2021) suggest that their findings propose a potentially bidirectional relationship between the acquisition of morphology and phonology, challenging the earlier assumption that phonological acquisition solely drives morphological acquisition. As Tessier (2016:1) points out, acquiring morpho-phonological patterns presents challenges both to learners and researchers as “the learner must determine a set of lexical representations attached to meanings, and also control the phonological regularities involved in the combinations of those stored representations”. In other words, morpho-phonological learning is inherently more complex than phonological learning. While it is possible to account for across-the-board phonological alternations by the phonological grammar alone, morpho-phonological patterns necessitate the integration of morphology, semantics, and phonology. For instance, consider sequences involving two morphemes verb + X, such as talk+[-t] and log+[-d]; the complexity in mastering the alternation of forms X arises from several interrelated components. It is essential to acknowledge that developmental processes are more entangled and iterative than linear in reality. These components can be learned synchronously or asynchronously, as Kim and Sundara (2021) show learning can be concurrent across domains. Regardless of the relative order of acquisition in the developmental path of learning allomorphy, the key components that an ideal 9 learner must acquire along their path to master the variations of the English past tense suffix2 is outlined in (7). (7) a. These sequences are comprised of 2 morphemes: verb + morpheme X. b. Morphemes talk and log are verbs with their respective meaning. c. Morphs [-t] and [-d] are similar in form (broadly speaking phonological similarity is not a requirement for allomorphs, but can be used as a cue in some cases). d. Morphs [-t] and [-d] share the same meaning (or syntactic function). e. Distributions of [-t] and [-d] follow a phonological pattern ([-t] after a voiceless non-sibilant C; [-d] after a V or voiced non-sibilant C). f. Morphs [-t] and [-d] should be represented and stored in the lexicon as variants of one morpheme <+past tense> and not separately. In certain instances, alternations related to a morpheme may adhere to the phonotactic rules of the language. For example, the acquisition of past tense allomorphs in English aligns with learning static restrictions found in mono-morphemic nouns about similarity in voicing in sequences of adjacent obstruents. Therefore, discovering the phonological basis for these alternations can, at least theoretically, be informed and guided by phonotactic learning. Empirical support for this issue is illustrated in a series of experiments by Chong (2021) where participants learned the alternations across morpheme boundaries best when the patterns matched the stem-internal phonotactics. However, it is common for phonological alternations to be limited to specific morphemes, presenting an additional challenging component for learners to resolve along with the components in (7a−f). As discussed in the previous section, the case of French liaison exemplifies this phenomenon. The latter half of this subsection focuses on the research related to the acquisition of French liaison. Various scholars have explored the early development of this morpho-phonological pattern utilizing both corpus data and experimental methodologies (Buerkin-Pontrelli et al., 2017; Demuth and Tremblay, 2008; Dugua, 2006; Chevrot and Fayol, 2001; Morel, 1994). This review will succinctly examine recent studies that aim to explain and characterize the errors associated with representations of prenominal liaison and nouns that begin with vowels. Evidence from perception experiments using a preferential-looking paradigm, as designed by Babineau and Shi (2014), indicates that children as young as 2;0 year of age familiarized with novel pseudo-words in various liaison contexts (which could be ambiguous between being vowel- 2 The facts about the acquisition of the past tense allomorphs in English are more complicated than presented here schematically with two of the forms (see Tomas et al., 2017; Oetting and Horohov, 1997). 10 initial or consonant-initial) accepted both segmentations of pseudo-words. For instance, in case of phrases like un onche [œ̃.nõʃ] or des onches [de.zoʃ], the pseudo-word onche could be ambiguous between combinations of [œ̃]+[nõʃ] where the syllable boundary and word boundary are aligned or [œ̃n]+[õʃ] where they are not. In contrast, 1;8 year old children tend to segment these novel words as consonant-initial (e.g., [nõʃ], [zoʃ].). More recently, Babineau et al. (2023) conducted follow-up experiments using different familiarization conditions with 2;0 year olds to shed light on the nature of their knowledge regarding liaison. Specifically, the goal was to determine whether their knowledge is shaped by language-specific statistical information from sub-syllabic distributions in French or whether it is not based on language-specific information per se and is only using broad statistical sub-syllabic distributions. If the children use their language-specific knowledge they could leverage it to overcome the universal bias influencing their segmentation which aligns syllable onsets with word edges. Their findings support the notion that, at this age, infants can recognize the co-occurrence patterns particular to certain liaison consonants in French in a larger context (including the first words) from which the sub-syllabic distributions emerge while disregarding the universal segmentation bias. However, this advanced top-down processing that resembles adult understanding is not as evident in the production of the toddlers of the same age as the authors also point out. Now before turning to the two different models discussed in the literature to explain and predict the production of French-speaking children, I will summarize the main error categories and empirical facts for young children as documented in different corpora. The rate of production errors during the first two years of life indicates that mastering liaison takes considerable time and often extends beyond two years. Buerkin-Pontrelli et al. (2017) analyze and report data from the Lyon corpus (Demuth and Tremblay, 2008) in CHILDES database (MacWhinney, 2000), categorizing the errors into two main types: a. those that involve phonological processes such as truncation or reduplication (e.g., les ami [le.mi] or [le.ma.mi]); and b. other errors related to the liaison consonant, such as insertion, replacement and omission (e.g., joli ami [ʒɔ.li.na.mi], les ami [le.na.mi], les enfants [le.ã.fã]). Their analysis reveals that during the early stages until 2;0 the errors are predominantly of a phonological nature to fill the onset positions of V-initial words or preserve minimal-foot structure. Between the ages of 2;0 to 3;0, errors involving liaison consonants appear in the children’s speech within the corpus. Further than 3;0, however, available data from one child in the corpus demonstrates that such errors are comparatively rare between the ages of 3 – 3;5. They highlight that those phonological errors (truncation and reduplication) were more common than liaison consonants errors, however the overall trajectory of the errors could suggest that as children’s phonological system stabilizes, they might produce errors which are directly due to their early awareness of liaison. One important point to keep in mind with regards to these studies is that the estimated age of mastery varies depending on whether the data is elicited or produced spontaneously. The spontaneous liaison 11 errors documented might decrease in earlier age ranges compared to elicited errors in experimental settings that could be even found with children tested up to 5;2. Buerkin-Pontrelli et al. (2017) also present results from an original experiment to investigate whether 3;0 children could produce two novel vowel-initial words in both liaison and non-liaison contexts productively. Their findings reveal that 3;0 children are reaching adults’ accuracy rate in full phrase contexts, which suggests they can segment and use liaison after a brief exposure. On the other hand, two-thirds of the children’s errors involved replacements or insertions, contrasting with adults, who tended to make more errors by omitting the liaison consonant. This indicates that children struggle more than adults to provide vowel-initial forms in non-liaison-triggering contexts. There are two models put forward in the literature to explain children’s acquisition of liaison. One model has examined the stages of learning liaison through a phonological lens (Buerkin-Pontrelli et al., 2017; Wauquier-Gravelines and Braud, 2005). With this model, the stages of acquisition are based on the evolution of syllabic templates. It is argued that following the maximum onset principle, children rely on distinct mechanisms in their errors to resyllabify word-final consonants in the word resulting in V.CV syllables rather than VC.V syllables. According to this model, once the phonological development is more complete, by ages 3;0 to 3;5, children can utilize morphological bootstrapping, enabling them to identify morphemes and the contexts in which particular liaison consonants (LCs) appear. The second model follows a constructionist approach (Chevrot et al., 2009) couched within usage-based theories (Tomasello, 2003) and argues that the acquisition of liaison occurs in three stages. In this framework, it is predicted that children store schemas (such as les + X, un + X) without information about the liaison consonant in determiners and alternating noun variants from 3;0 to 5;0. By the ages of 4;0 to 5;0, they begin to develop schemas that reflect the relationship between a determiner and a class of noun variants (e.g., les + /zX/, un + /nX/). As Buerkin-Pontrelli et al. (2017) indicate, the expected timelines for these stages in the constructionist model are not entirely precise, as children tend to exhibit fewer liaison errors after the age of 3. However, constructionist models heavily depend on input frequency, leading to the prediction that certain nouns are more closely associated with errors in singular contexts than with plural. As supported by the results of the experiment reported by Buerkin-Pontrelli et al. (2017), input frequency plays a role in early stages of learning; however, its role and its interaction with other aspects of learning more complicated patterns such as liaison needs further investigation. In the next section, before I discuss a proposal regarding how the phonological grammar can enable the learning of liaison-like patterns—and to what extent it can do so, along with the predictions it generates for the experiment—I will first provide an overview of the nature of the learning problem. 12 2.4. Learnability of liaison as a morpheme-specific phonological phenomenon within Optimality Theory The logical problem of language acquisition as summarized by Kager (2004: 323) from the original work on learnability in Optimality theory (Tesar and Smolensky, 2000) concerns learning three factors as shown in Figure 2-1: a. output representations; b. underlying representations; c. constraint hierarchy. These factors are assumed to be interdependent which means that learners in principle use iterative strategies to be able to go back and forth between these elements. Fundamentally, as Tesar and Smolensky (2000) introduced this problem, learning could be decomposed along some dimensions with processes that must interpret the hidden structure of the output (robust parser component) and compute the optimal structure for the underlying form (lexicon learner component) through the constraint hierarchy (grammar learner component). Morphophonemic learning in contrast to phonotactic learning involves an additional layer of morphological information, specifically when deriving underlying representation. Consequently, learning idiosyncratic patterns of allomorphy involves interaction between different parts of linguistic knowledge, namely, the lexicon and phonology. Two aspects of learning, in particular, are of interest in this thesis for an account that deals with the learnability problem of morpheme-specific alternations like liaison. Firstly, as demonstrated by the data in section 2.2, the idiosyncratic nature of external allomorphy patterns like liaison can be attributed to their extended domain. Mascaró (2004) highlights the paradoxes in this type of allomorphy with some examples from English which he refers to as external allomorphy. In the case of French liaison, to begin with, classifying word1s under liaison (allomorphy) or non-liaison (non-allomorphy) classes is not predictable by surface phonological forms. A lexical solution enables the learner to solve the problem for similar cases of unpredictability, for instance, regular vs. irregular past tense verbs in English: walk/walk-ed, talk/talk-ed vs. buy/bought, bring/brought. In cases when some verbs do not take the regular allomorph (-ed suffix), the past tense suppletive allomorph is listed in the lexicon. Whereas in liaison, a similar lexical solution does not suffice; learners must be aware of a bigger domain that Figure 2-1. Interdependence of the three factors of output, underlying representation and constraint hierarchy in language acquisition taken from Kager (2004:323) 13 extends beyond the word1 and includes the adjacent right word. For any given word1, the learner needs to know when to apply the allomorphy by considering if the word2 is C/V-initial. In other words, the learners would not be able to simply list every word1 + word2 phrase in the lexicon as they might do with the English irregular past tense forms. Even though the classification of each word1 under allomorphy or non-allomorphy could seem rather arbitrary to the leaner and without any phonological motivations, phonological optimization is important for the participating word1s in liaison that do have an allomorphic pair. Predicting the choice of the allomorph in liaison patterns is possible through the lens of phonological optimization as it is natural to create forms that are following the most unmarked outcome in terms of syllable structure. However, if phonology is emerging to create an optimal structure in the larger prosodic domain of the allomorphy, the puzzle remaining for the learner is now the following question: why is it only restricted to just a limited set of lexical items? Simply stated, in the current case study, the lexical and arbitrary nature of allomorphy itself creates an arbitrary partition in the phonological grammar as shown in Figure 2-2. On the one side of the grammar, in the closed lexical set of liaison morphemes, prioritizing optimal structures in the grammar with constraints on markedness is required. While on the other side, in morphemes outside that closed lexical set, it is not. In the learning theory outlined below in the following subsections, I aim to address how this issue could be managed within the learner's grammar. The current proposal involves a mechanism based on constraint indexation (Pater, 2010) applied to the learning of liaison. The second rather unique property of liaison pertains to the locus of the alternation in the allomorphs along with the order of the of specific morphemes relative to each other. As seen in examples (1‒4) in Section 2.2. liaison is an external sandhi phenomenon which occurs in a domain of two morphemes where the first morpheme exhibits alternation on its right edge (e.g., high markedness constraints required(liaison)[pəti]/[pətit][le]/[lez]...low markedness constraints required (non-liaison)[ʒɔli][ʒoen]...Figure 2-2. Partition in the phonological grammar for word1s in liaison or non-liaison classes 14 [peti]~[petit]), bordering the left edge of the second morpheme. When the second morpheme begins with a vowel, the liaison consonant is resyllabified as an onset of the second morpheme. Therefore, especially in noun phrases where the second morpheme is a vowel-initial noun, the noun can be resyllabified with different onsets every time it is combined with a variety of liaison consonants in different contexts. Similar patterns are found in Celtic languages, which exhibit initial consonant mutation on their nouns in different contexts such as with pronouns or prepositions (Hannahs, 2011). However, such patterns are relatively uncommon and less widespread typologically compared to other cases of external allomorphy, where suffixation is more prevalent. As observed in the developmental trajectory of learning liaison, this presents challenges in the initial stages of learning morpho-phonological phenomena for learners, making it particularly challenging to correctly represent the input forms of morphemes involved in liaison. In the following subsection, a detailed discussion of the issue regarding the input and its crucial role in a learnability account with an OT-based learning algorithm is presented. This is followed by an illustration of the formal properties that such a grammar must possess to enable learning. 2.4.1. Learning the underlying representation In the course of acquisition, a learner must simultaneously learn the ranking and the lexicon. The latter has been incorporated into the system as identity mapping based on the principle of lexicon optimization (Prince and Tesar, 2004). When learners are faced with no evidence of overt alternations, the chosen underlying form among possible input forms is the one that makes the most faithful input-output mapping. Learning the underlying representations of morphemes is crucial to the process of learning the allomorphy, as “the underlying representations influence the grammar and the grammar influences the underlying representations” (McCarthy, 2005: 25). However, it is important to note that in a real-life scenario of language acquisition, morphological analysis and segmentation must be integrated with other aspects of learning. Leveraging the paradigmatic information in the alternation for computing the underlying representation seems accessible to the analyst. However, it is deemed to be tractable for learners only at a stage where they have made progress in understanding the semantics and segmentation of the phrases they encounter as overt forms. In cases of allomorphy, the underlying representations of morphemes and the alternation are highly interdependent and “have to be inferred from combined analytic assumptions about the output and the constraint hierarchy” (Kager, 2004: 322). To expand on this, it is useful to first consider a less complex example of allomorphy as a point of comparison where the alternation is 15 motivated by a phonotactic constraint in the language3. In the previously mentioned example of the English past tense allomorphs (e.g., walk[t], jog[d], etc.), the conditions for the voicing alternations are true such that the suffix’s alveolar consonant is voiced after a voiced consonant and voiceless after a voiceless consonant. This distributional restriction also occurs within clusters in mono-morphemic words which are always similar in voicing. Having successfully learned the phonotactic constraints rankings governing the distributions of phonemes, in early stages of morphophonemic learning the learner needs to recognize the past tense morpheme as a suffix which means an underlying representation must be specified. Failing to select the appropriate underlying representation could result in the learner's inability to learn the alternation given its existing constraint ranking. Theoretically, in the process of learning, when the learner makes errors on an alternation, two possible scenarios exist: either the constraint ranking within the grammar or the underlying representation would need to be revised. For the learners of the regular past tense allomorphy in English, modifying the grammar implies revising the constraint hierarchy which had been successful for mono-morphemic words. Any other constraint hierarchy would not be consistent with the rest of the learning data in English as a modified ranking could not apply to both the mono-morphemic words and words including the past tense suffix. Therefore, out of the two choices, the underlying representation is more likely to be revised. For learners of French, however, part of the challenge lies in the fact that liaison is not motivated by a phonotactic generalization that is language-wide. Furthermore, if the learner is to revise its underlying representations, as mentioned before, the unique location of the alternation in French liaison presents an additional layer of complexity for segmentation, which complicates the learning process of deriving underlying representation. The information provided in the examples below can be categorized into two types: morphemic contrast and morphemic alternation (Tesar, 2014: 247). The following paradigm in (8) provides an opportunity for the learners to utilize the morphemic alternation information and compare phrases demonstrating diverse contexts for the same morpheme (in this case, plural determiner /le(z)/). (8) a. les bébés [le.be.be] ‘the babies’ b. les amis [le.za.mi] ‘the friends’ c. les ours [le.zu.ʁs] ‘the bears’ 3 See Kager (2004: 330-336) for an example of a learner with a morphological handicap which shows that the algorithm would still converge when learning the voicing alternation in plural morphemes in Dutch. 16 To recognize the variation in the forms and to determine that both [le] and [lez] are two possible outputs for the same morpheme indicating the plural determiner, learners need to rely on their understanding of the underlying forms of the morphemes /bebe/ and /uʁs/ or /ami/. However, if the learner has not fully computed the underlying forms in the morphemic contrast paradigm for both the vowel-initial nouns (e.g., /uʁs/) and the consonant-initial nouns (e.g., /bebe/), their ability to learn the multiple representations for the allomorphy will be impacted. The issue specifically arises with vowel-initial nouns and their position. In the following contrastive paradigm in (9), the learners observe the noun /uʁs/ preceded by different morphemes. In this paradigm, the left edge of this noun in French is occupied by various liaison consonants (9a−c), except when it is adjacent to a non-liaison word1, as in (9d) with [ʒɔli]. This ordering results in an unstable position for the onset of the second word which has the potential to be rebracketed by the learners, as discussed in section 2.3. Understanding that these nouns do not have several C-initial variants and are in fact V-initial requires resisting the segmentation that aligns the onset of the nouns with the onset of the syllable. In phonological theories, aligning the onset of syllables and morphemes is part of the general alignment framework in the universal markedness constraints (McCarthy and Prince, 1993; Tesar and Smolensky, 2000). Consequently, particularly in early acquisition, it might not be surprising that this position of alternation contributes to how this issue is intuitively challenging to overcome. Furthermore, the role and saliency of onsets is also supported by various other psycholinguistic models of lexical segmentation such as the Syllable Onset Segmentation Hypothesis (Content et al., 2000), Shortlist B (Noris and McQueen, 2008).In the context of French liaison, the majority of word2s belong to an open class of lexical items (non-functional). Therefore, the need to resist alternations at the left edge of the word2s is crucial for the learning of the lexicon. As noted by Babineau et al. (2023: 305), “French liaison violates this universal constraint, as liaison sacrifices to some degree the number of minimal pair words in the lexicon”. This also has direct implications for the task of morphological parsing and learning the underlying representations. For example, English learners can infer, due to this bias, that a set of minimally different words like foul, cowl, howl are separate words and not just variants of a vowel-initial word like owl. Conversely, for French learners, syllables like [zuʁs], [tuʁs], [nuʁs] are not separate words, but rather all share the same vowel-(9) a. les ours [le.zuʁs] 'the bears' b. un ours [œ̃.nuʁs] 'a bear' c. petit ours [pə.ti.tuʁs] 'little bear' d. joli ours [ʒɔ.li.uʁs] 'nice bear' 17 initial word [uʁs]. Babineau et al. (2023) also note that this issue is not particularly severe, as the number of possible liaison consonants that can lead to ambiguous syllabification in French is limited to a few consonants. By examining the issues surrounding underlying representations and segmentation, I have illustrated that learners must navigate the tension between language-specific properties and universal constraints in order to progress along the correct path. In the following subsection, I will propose a heuristic that could lead to a bias under which learning the underlying representations can be achieved for successful learning, and delve into the components of the initial state grammar along with the trajectory to the end state grammar. 2.4.2. Initial state grammar to end state grammar In the initial state of the grammar, markedness constraints fully outrank faithfulness constraints. This initial state is adopted as it is well-supported by the evidence in the literature of phonological acquisition in Optimality Theory. Smolensky (1996a; 1996b) and Gnanadesikan (1995) suggest this initial state can account for both children’s production and comprehension. It also makes better predictions for learning with no positive evidence of alternations per the Subset Problem (Smolensky, 1996a, Prince and Tesar, 2004). This assumption is also connected to the richness of the base principle in Optimality theory where any imaginable input may be considered since the outputs are constrained by the interaction of constraints. Davidson et al. (2004) report results from experiments on the processing of infants and adults showing that this principle and its consequences for the initial ranking are supported by human linguistic performance. Apart from this traditional assumption, other possibilities within the literature include an unranked state or faithfulness constraints outranking markedness (Hale and Reiss, 1997). In this analysis, I propose an initial state where all the learners of French start with the schematic Markedness >> Faithfulness constraint ranking with the constraints introduced below in (10). (10) The initial state grammar G0: a. Markedness constraints: all speakers have structural constraints for the most unmarked syllable structure (CV.CV): NoV.V4, NoC.C5 as well as alignment constraints Align-L6. 4 No V.V: Mark a violation if two hetero-syllabic vowels are adjacent (V.V). 5 No C.C: Mark a violation if two hetero-syllabic consonants are adjacent (C.C). 6 Align-L: Mark a violation if the left edge of a morphological word does not coincide with the left edge of a prosodic word (Kager, 2004: 111). 18 b. Faithfulness constraints: all speakers have constraints that control the input-output correspondence (i.e., penalizing deletion and insertion of segments): Max7, Dep8. c. These classes of constraints are ranked such that markedness constraints dominate the faithfulness constraint (M >> F): NoV.V, NoC.C, Align-L >> Max, Dep In order to tackle the questions of learning morpho-phonological patterns, I focus on basic examples of prenominal configurations introduced above in section 2.2, such as the common sequence of the plural determiner [le]/[lez] + nouns. Beginning from a universal initial state typical of learners of all languages, how does the grammar of learners of French develop as they are exposed to French-specific phonological patterns until they have fully learned morpheme-specific phonological alternations like liaison? The analysis provided here incorporates a mechanism that enables learners to recognize and address inconsistencies in their grammar adopting Pater (2010). This analysis is also informed by additional biases in two places, which will be elaborated upon later throughout this subsection. The learning algorithm implemented in the current analysis follows the biased error-driven constraint demotion algorithm (Prince and Tesar, 2004; Hayes, 2004). Implementing this algorithm, not only does the learner start with a markedness bias in its initial state, but it is also biased towards the markedness constraints during reranking stages or constraint demotion. In the early stages of phonological development, as discussed in section 2.3, children learn language-specific phonotactics. For my analysis, I assume that prior to learning morphology, French learners acquire some phonotactic and distributional information about their language, which informs their language-specific knowledge. This suggests that during this early stage of learning, out of a tendency to maximize lexicon optimization, the initial bias of highly ranked universal constraints favouring unmarked structures would be gradually overridden by the set of constraints related to being faithful to the input form of words. In the error-driven process of learning, among the sets of phrases that contribute to learners’ language-specific phonotactic knowledge is the non-alternating adjective + nouns in our examples. The non-alternating class of morphemes in general involves an open class of lexical items, making them shape most of the lexicon as they are more frequent type-wise. A learner who encounters phrases such as jeune bébé and joli ami as well as many other similar verbal or prepositional phrases (containing V.V and C.C syllable patterns) simply stores each new word they learn in the input as is, based on the principles of lexicon optimization. The relevant errors learners make with regard to these phrases lead them 7 Max: Mark a violation if every segment in the input does not have a corresponding segment in the output. 8 Dep: Mark a violation if every segment in the output does not have a corresponding segment in the input. 19 to updating the initial state constraint ranking. During the update, the biased constraint demotion algorithm imposes a bias in favour of markedness constraints, therefore they are not to be demoted as long as possible To illustrate how an ideal learning trajectory progresses at each step with an error-driven algorithm, first a table of error archives is presented, and then after resolving the errors, some example tableaux are provided with the new updated grammar at each stage. The table below shows the error archive and provides a pair of candidates consisting of the winning candidate (the observed output) and one losing candidate selected by the current grammar for each input. Each row in this error archive, which is known as the error, indicates whether the constraints prefer the optimal winner (W) or the suboptimal competitor, the loser (L). The novelty in my analysis is the first column in the table called “Error by Current Grammar” which notes whether the errors present in the error archive were made by the current state of the grammar. The current grammar of the learners, written on top of the table, has led them to the errors marked by . Importantly, the concept of an error archive refers to a kind of permanent storage accessible to the algorithm where learners record their errors. If at any point during learning, the algorithm reads the archive and an error lacks any marks in the first column, it means that it has been archived in previous stages. At the same time, the inputs of input-output mappings that do not make it into the error archive are stored directly in the lexicon also accessible in phonological learning. At this point, the current grammar is the initial state grammar stated in (10). (11) Error archive with errors of the CG (NOV.V, NOC.C, ALIGN-L >> MAX, DEP) Error by CG Input W ~ L NOC.C NOV.V ALIGN-L MAX DEP  a. /ʒɔli+ami/ ʒɔli.ami ~ ʒɔli.zami L W W  b. /ʒɔli+ami/ ʒɔli.ami ~ ʒɔ.lami L W W  c. /ʒœn+bebe/ ʒœn.bebe ~ ʒœ.bebe L W  d. /ʒœn+bebe/ ʒœn.bebe ~ ʒœni.bebe L W  e. /ʒœn+ami/ ʒœ.nami ~ ʒœ.ami W L W As can be seen from the errors above, the very initial state grammar leads the learner to select these losing candidates which have unmarked syllable structures. Once new errors enter the error archive marked by , the error-driven algorithm then requires an update and initiates a new constraint hierarchy according to the violation profiles of each candidate pair in terms of their constraint preference. With the biased constraint demotion algorithm, markedness constraints have priority to be placed at the top of the new stratum of the constraint hierarchy provided they prefer no losers. However, this is not the case at this stage, as there are not any markedness constraints 20 which would prefer no losers. Whereas faithfulness constraints, Max and Dep, prefer the winning candidates of the pairs in each error. It is worthwhile to note that including errors that result in reranking Align-L in the first error archive, as seen in cases like error (11e) serves the purpose of providing a comprehensive analysis of all constraints. However, realistically, during the initial stages of phonotactic acquisition, learners may not be fully aware of morphological boundaries within phrases9. In this update, the resulting crucial constraint ranking in (12), achieved by the learner during the phonotactic learning stage, ensures that such errors are not being made anymore moving forward. Thus, all the errors in (11a-e) are then successfully archived. (12) Phonotactic Grammar: DEP, MAX >> NOV.V, NOC.C, ALIGN-L /ʒœn/+/bebe/ DEP MAX NOV.V NOC.C ALIGN-L ☞ [ʒœn.bebe] * [ʒœ.ni.bebe] *! [ʒœ.bebe] *! /ʒœn/+/ami/ DEP MAX NOV.V NOC.C ALIGN-L ☞ [ʒœ.na.mi] * [ʒœ.a.mi] *! * /ʒɔli/ +/ami/ DEP MAX NOV.V NOC.C ALIGN-L ☞ [ʒɔ.li.a.mi] * [ʒɔ.li.za.mi] *! * [ʒɔ.la.mi] *! * The important argument made here for the grammar in (12) is based on a reasonable assumption that when learners arrive at the inconsistency between liaison and non-liaison morphemes, they already possess a not-so-naïve grammar. The grammar with which they enter morphophonemic learning is not exactly the same as the initial state grammar and has undergone some modifications. This is illustrated in the tableaux above and evidenced by an error archive that accumulates as they encounter simple phrases during phonotactic learning. Gradually, learning the underlying representations of the alternating morphemes becomes more feasible for the learner after gaining some knowledge about the phonotactics and the lexicon. 9 This constraint would be accessible in phrases where morphological knowledge is acquired. Learners have to know the prosodic word with a syllabification of /n/ for an output such as [ʒœ.#na.mi] is not aligned with the morphological boundaries in the output [ʒœ.n#a.mi]. 21 When learners develop a certain level of awareness regarding morphological parsing through semantic or visual cues in the real world, they start forming hypotheses about the additional morpheme they have identified before the nouns in determiner + noun phrases. In other words, the learner eventually must realize that the phrases les amis and les bébés are not monomorphemic and contain more than one morpheme. At the same time, they could conclude that the first morphemes of these phrases are, in fact, semantically related and function as determiners. Incidentally, one type of evidence that can aid them in learning the underlying representation of the alternating liaison morphemes could come from the knowledge of nouns’ underlying representations, especially when learners compare different contrastive paradigms in (9). For instance, as learners become more proficient in understanding the representations of the nouns, they may find it more likely that among the forms they had encountered for the noun ‘friend’ (e.g., [tami], [zami] and [ami]), the underlying representation is /ami/ rather than the other C-initial forms. This realization could in fact lead them to segment the phrases correctly and discover that the first morphemes in phrases like /lez+ami/ or /le+bebe/ are not only semantically related, but are actually the same morpheme. By exploring different options for the underlying representations of the determiner, learners can formulate a range of hypotheses. First, I propose that learners prefer to maintain a single underlying representation rather than positing multiple ones. This approach narrows the hypotheses window and it simplifies the learning process by shifting the responsibility of learning onto the grammar, rather than requiring extensive storage in the lexicon. In this scenario, learners would be faced with two possibilities and they must select one as the underlying form: either the input is shaped as CVC or CV. The two tables below are provided just to illustrate the comparison between the larger input in CVC form (13a-d), and the smaller input in CV form (13e-h). If the learner takes the hypothesis of larger allomorph as the input such as /lez/ or /œ̃n/, the resulting errors would have the following preferences where Dep is indifferent with respect to winners or losers. (13) Input W ~ L NOC.C NOV.V ALIGN-L MAX DEP a. /lez/ + … le.zami ~ le.ami W L W b. le.bebe ~ lez.bebe W L c. /œ̃n/ + … œ̃.nami ~ œ̃.ami W L W d. œ̃.bebe ~ œ̃n.bebe W L If the learner takes the hypothesis of the smaller allomorph as the input such as /le/ or /œ̃/, the resulting errors would have different preferences where Max is indifferent with respect to winners or losers. 22 (13) Input W ~ L NOC.C NOV.V ALIGN-L MAX DEP e. /le/ + … le.bebe ~ lez.bebe W W f. le.zami ~ le.ami W L L g. /œ̃/ + … œ̃.bebe ~ œ̃n.bebe W W h. œ̃.nami ~ œ̃.ami W L L My proposed heuristic could be in form of a bias in favour of storing the unpredictable information in the input by maximizing the structure encoded in the input. Under this heuristic, the larger allomorph /lez/ or /œ̃n/ (13a-d) would be the best underlying representation among the possible input forms. In other words, in instances of determiner + V-initial noun combinations when the learner has the opportunity to encounter the allomorph form with a maximal structure (here the CVC form), that should be the preferred choice10. With this input the grammar relies on satisfying the NOC.C constraint at the expense of MAX, that is, not being faithful to the input by deleting the final consonant11. Other existing alternative analyses in the literature regarding French liaison in an OT-based grammar employ other mechanisms such as constraints for the UR (Smith, 2015) or multiple URs (Storme, 2024). However, applying this simple heuristic renders the input in conjunction with the ranking in the grammar learnable. As a result of choosing the larger allomorph for the underlying representation, learners are left with errors with the error proflies exemplified below in (14). Note that the other faithfulness constraint DEP is not playing a role among the crucial constraints anymore. 10 It is worth mentioning that the literature is non-conclusive regarding this general criterion, so testing this heuristic in this specific domain needs further experimental investigation. The past literature in OT on what possible constraints can exist in Con has put forward a constraint family known as *Struc (Prince and Smolensky, 1993) which has a “less is best” spirit. In this situation it would mean selecting the other possible input in CV form to be the underlying representation as it is structurally less complex. However, this view is not the established view in the literature as Gouskova (2003) has shown in her work. 11 Choosing the smaller allomorph as the input, entails that the learner has to choose a grammar that ranks No V.V >> Dep. In this grammar, generating the other allomorph necessitates inserting the final consonant (LC) which makes the phonological learner reach a dead-end very soon, since it eventually becomes evident that each morpheme requires insertion of an arbitrary consonant. For instance, for the masculine singular indefinite article un a hypothetical learner could choose the nasal segment /n/ to be inserted because the vowel is nasalized. However, by inserting the same nasal segment in the plural definite morpheme les the learner would be making an error. 23 (14) Input W ~ L NOC.C NOV.V ALIGN-L MAX DEP a. /lez+ami/ le.zami ~ le.ami W L W b. /lez+bebe/ le.bebe ~ lez.bebe W L To continue learning and to achieve a stable end-state of the grammar, the learner must reconcile the morpheme-specific constraints in two conflicting rankings within its grammar. In my current learnability analysis, I incorporate a mechanism borrowed from Pater's (2010) constraint indexation model of Optimality Theory to analyze morpheme-specific phonology and exceptionality. He argues that this approach to morpheme-specific phonology offers advantages over previous proposals such as co-phonologies by Inkelas and Zoll (2007). Although similar mechanisms of indexation have been previously proposed by Fukuzawa (1999) and Ito and Mester (2001) for faithfulness constraints, Pater's (2010) version allows both markedness constraints and faithfulness constraints to be lexically indexed if necessary. According to this approach, inconsistencies can be identified and resolved as the learner encounters them through facing errors during the learning process. The error archive below demonstrates a winner-loser pair for each input, representing the two classes of morphemes. The inconsistency is evident in error rows bolded (15c vs 15d) as there is not a consistent constraint that prefers only Ws. Here each constraint favours a morpheme belonging to a different class and the reranking algorithm reaches a halt. The current grammar of the learners making the last two errors (15d-e) marked below with  is the grammar after phonotactic learning in (12). The other rows (15a-c) are the previous errors stored in the error archive12. (15) Error archive with errors of the CG (MAX >> NOV.V, NOC.C, ALIGN-L) Error by CG Input W ~ L MAX NOC.C NOV.V ALIGN-L a. NL W1: /ʒɔli+ami/ ʒɔliami ~ ʒɔlami W L W b. NL W1: /ʒœn+ami/ ʒœ.na.mi ~ ʒœ.ami W W L c. NL W1: /ʒœn+bebe/ ʒœn.bebe ~ ʒœ.bebe W L  d. L W1s: /lez+bebe/ le.bebe ~ lez.bebe L W  e. L W1s: /lez+ami/ le.za.mi ~ le.ami W W L Following the instructions in the algorithm under Pater’s (2010: 20, ex 48) account for inconsistency resolution, the learner must perform the instruction given in (16). 12 The idea is that all errors are permanently stored in the error archive; however, for space reasons, errors in (11a) and (11d) are not displayed since Dep is no longer included in the constraint set. 24 (16) Clone a constraint that prefers only Ws in all instances of some morpheme, and index it to every morpheme for which it prefers only Ws. As Pater notes in his work, an aspect of constraint cloning remains to be fully elaborated. Particularly, how does the learner proceed when the choice of the constraint to be cloned is not straightforwardly down to one single constraint? The appendix in the original work by Pater (2010) reviews procedures that could be performed by the algorithm (borrowed from linear programming) during learning when the algorithm can not decide which constraint to clone to resolve the inconsistency. He also discusses one option to be the inclusion of an “exceptional” bias targeting the smallest set of morphemes to help the learner choose one solution over the other depending on the lexicon, but he concludes that this procedure needs further research. My analysis includes the proposal of a bias which could enable the learner to decide among equally available options for constraint cloning. This bias is shaped by considering the current grammar which is itself driven by earlier errors in the error archive. An explicit adjustment to the previous statement is stated in (17). (17) Clone the constraint that prefers Ws in all instances of the errors committed by the current grammar and index it to morphemes for which it prefers only Ws for those errors. The minimal inconsistent pairs of errors for French learners /lez+bebe/ and /ʒœn+bebe/ are shown again in a new table below in (18). (18) Minimal inconsistent pairs of errors by the CG (MAX >> NOV.V, NOC.C, ALIGN-L) Error by CG Input W ~ L MAX NOC.C NOV.V ALIGN-L NL W1: /ʒœn+bebe/ ʒœn.bebe ~ ʒœ.bebe W L  L W1s: /lez+bebe/ le.bebe ~ lez.bebe L W At this juncture, the choice of cloning the winning preferring constraint is not apparent. The two options below are both equally available to the learner to resolve the inconsistency: a) Clone No C.C indexed to liaison W1s (e.g., /lez/) b) Clone Max indexed to non-liaison W1s (e.g., /ʒœn/) As mentioned before, the important assumption taken for granted is that learners of French have a different (more mature) grammar from the initial state grammar at the point when they reach this inconsistency. As can be seen from the winner~loser pair above, currently, non-liaison 25 word1s do not lead to an error by the learner anymore as the W preferring constraint for them is MAX which is highly-ranked in the current grammar. A word1 in the liaison class (L W1) is the recent error made by the current grammar. Therefore, guided by the bias introduced in (17) they must clone the constraint preferring Ws for the liaison word1 morpheme (NOC.C), as it is the error committed by the current grammar and index it to that morpheme (NOC.C-L). The clone constraint is added to the constraint hierarchy as shown in (19). (19) Error by CG Input W ~ L NO C.C-L MAX NO C.C NO V.V ALIGN-L a. NLW1: /ʒɔli+ami/ ʒɔliami ~ ʒɔlami W L W b. NLW1: /ʒœn+ami/ ʒœ.na.mi ~ ʒœ.ami W W L c. NLW1: /ʒœn+bebe/ ʒœn.bebe ~ ʒœ.bebe W L  d. LW1s: /lez+bebe/ le.bebe ~ lez.bebe W L W  e. LW1s: /lez+ami/ le.za.mi ~ le.ami W W W L Now with the new cloned constraint present, the reranking procedure in the update can be restarted. I will illustrate the biased constraint demotion algorithm here step-by-step. Among markedness constraints, the NOC.C-L constraint is placed on the top stratum, shown in (20), as it is the only markedness constraint that prefers only Ws in an instance of some morpheme. After this constraint is placed at the top of the hierarchy the relevant errors in rows (d-e) would technically be resolved and successfully archived. (20) No C.C-L >> Error by CG Input W ~ L NO C.C-L MAX NO C.C NO V.V ALIGN-L a. NLW1: /ʒɔli+ami/ ʒɔliami ~ ʒɔlami W L W b. NLW1: /ʒœn+ami/ ʒœ.na.mi ~ ʒœ.ami W W L c. NLW1: /ʒœn+bebe/ ʒœn.bebe ~ ʒœ.bebe W L  d. LW1s: /lez+bebe/ le.bebe ~ lez.bebe W L W  e. LW1s: /lez+ami/ le.za.mi ~ le.ami W W W L As the inconsistency is now resolved, the update can proceed with a similar procedure as before based on the winner~loser pairs in (20a-c). No markedness constraint prefers only Ws, therefore the faithfulness constraint is the next constraint to be placed in the new stratum. At the 26 end, the learner has the hierarchy shown in (21) with a cloned constraint indexed to the set of morpheme(s) with the same index (here L chosen to stand for liaison morphemes). (21) No C.C-L >> Max >> No C.C, No V.V, Align-L *L: {/lez/, …} The two tableaux below (22) show examples of phrases attached to an indexed subset of the lexicon [lebebe] and [lezami]. Notice that the underlying representation of the word1 is the consonant-final form /lez/ which means NoC.C-L13 has to crucially outrank Max and Max has to in turn crucially outrank Align-L. (22) /lez/L+/bebe/ NO C.C-L MAX NO C.C NO V.V ALIGN-L ☞ [le.bebe] * [lez.bebe] *! * /lez/L+/ami/ NO C.C-L MAX NO C.C NO V.V ALIGN-L ☞ [le.za.mi] * [le.ami] *! * It is also worth illustrating in (23) that this new cloned constraint does not affect words like [ʒœnbebe] or [ʒɔliami] because it is only indexed to certain word1s (liaison word1s). (23) /ʒœn/+/bebe/ NoC.C-L Max NoC.C NoV.V Align-l ☞ [ʒœn.bebe] * [ʒœ.bebe] *! /ʒɔli/+/ami/ NoC.C-L Max NoC.C NoV.V Align-l ☞ [ʒɔ.li.a.mi] * [ʒɔ.la.mi] *! A crucial concluding step remains in this analysis. The process outlined above addresses the procedure for instances of a single morpheme. Although multiple liaison morphemes in French 13 I am assuming that the indexed constraints follow a locality principle and only apply locally to the morpheme indexed, here /lez/, and not to the full word1+word2 input. 27 need to be indexed, they constitute a finite set. Therefore, whenever learners encounter phrases containing new morphemes that fall within the same class as liaison words, such as the masculine singular indefinite article + noun in un ami, the same procedure applies to resolve any inconsistencies. In this case, the cloned constraints for each morpheme would essentially be duplicates of the NoC.C constraint and positioned within the same top stratum (24). (24) NO C.C-L2**, NO C.C-L* >> MAX >> NO C.C, NO V.V, ALIGN-L *L: {/lez/} **L2: {/œ̃n/} Therefore, we expect that learners may have the option to either merge or delete the extra constraints, ultimately retaining a single constraint linked to multiple indexed liaison words instead. The complete final grammar in the current analysis where learners would converge on an end state, including all the relevant constraints, therefore would be as in (25). (25) Final state grammar: NO C.C -L* >> MAX >> NO C.C, NO V.V, ALIGN-L *L: {/lez/, /œ̃n/, …} It is beneficial at the end of this subsection to highlight that several key points emerge from this analysis based on certain underlying assumptions regarding an ideal learner. Firstly, it is assumed that the learners are equipped with a universal biased M>>F ranking in their initial state which leads to their first errors during phonotactic learning. Subsequently, another assumption posits that as a result of successful phonotactic learning, the ideal learner maintains a specific ranking of the grammar at the time of encountering inconsistencies and during the learning of allomorphy. This ideal trajectory shapes the bias that enables the learners to successfully overcome the challenge of learning morpheme-specific alternations in this analysis. As previously mentioned, other alternative biases for learning indexation in morpheme-specific patterns according to Pater (2010) include a bias for the smallest set of morphemes or constraints. In this regard, it remains ambiguous whether a definitive solution exists for assessing the relative frequency of liaison morphemes compared to non-liaison morphemes, as well as whether such criteria could be appropriately applied to these morphemes in a phonologically conditioned allomorphy domain. Therefore, an additional crucial criterion favouring the errors made by the current grammar was introduced and incorporated in this analysis. In an earlier work on constraint indexation, Pater (2007:11) introduced the concept of constraint indexation in a context where the order of winner-loser pairs created by the learners is not explicitly addressed. He mentioned in a footnote that if a learner possesses an incomplete set of learning data, there is a risk of incorrectly cloning certain constraints. However, he then posits 28 that this would likely have minimal impact, as these constraints would eventually be ranked lower in the hierarchy if they do not contribute to resolving inconsistencies. To further explore this idea with hypothetical learning processes, I have devised various experimental scenarios that control the sequence in which participants are exposed to different types of learning data. Additionally, I ensured that the experimental environment did not allow learners to exhibit exceptional biases based on familiarity with the lexicon or frequency. In the following section, I will review these conditions and discuss the predictions derived from them, enabling comparisons based on participants’ accuracy and errors. 2.5. Predictions of the learning theory in the current study The current study aims to compare the learning of morpheme-specific phonological patterns across various controlled learning trajectories. The order in which learning data was presented to the participants was carefully controlled in an experimental setting designed to induce an inconsistency detection in the learner’s learning algorithm. Before expanding on my predictions regarding the different learning trajectories, it is important to establish the assumptions guiding the hypotheses. The most crucial assumption is that, in all learners in the experiment, the initial state aligns with the state described in section 2.4.2. This means that, rather than possessing a set of unranked constraints, learners exhibit strong biases toward the most unmarked syllable structure (CV.CV) (for related points about the methodology of artificial language learning experiment and to the extent where L1 biases are transferred, see Tang and Baer-Henney, 2023) . Therefore, I assume that in an experimental setting, the initial state of all learners follows the G0 below in (26) with faithfulness constraints being outranked by markedness constraints. (26) G0: NOC.C, NOV.V, ALIGN-L >> MAX Moreover, as per my analysis discussed above following Pater (2010), I assume that learners would update their grammar based on the learning evidence presented to them at any given point. This grammar operates within a single hierarchy of constraints, requiring learners to rerank their constraints and make updates when faced with new evidence of errors or of inconsistencies. In the experiment, I investigated three different learning trajectories, assuming all are starting from the same initial state grammar (26) but exposed to merely positive learning data. These trajectories involved receiving either both classes of morphemes at once or in an isolated manner, one by one. The learning data consisted of phrases in an artificial mini-language that included similar patterns to the morpheme-specific phonological patterns in French. This mini-language consists of four 29 word1s (two liaison, and two non-liaison) along with several word2s and its presentation to participants in the experiment is divided into two blocks (for more details, refer to Chapter 3). In the next subsections, I draw upon real French phrases to demonstrate the three learning trajectories and examine the outcome predicted by my hypotheses. 2.5.1. Ordered learning trajectory - Liaison first In this group of learners, the first block involves receiving two liaison morphemes while the second block includes the two non-liaison morphemes. In this manner, the initial evidence presented to learners based on what they encounter in the first block lacks any form of inconsistency. In the first block, the ideal learner who has established the semantic connection between the allomorphs needs to identify the larger consonant-final allomorph /lez/ and /œ̃n/ as the underlying representation when presented with the following set of phrases: {le+bebe, lez+ami, …, œ̃+bebe, œ̃n+ami, …}. By the end of the first block, assuming an initial state bias from G0, the learner does not make any errors with [lebebe] or [œ̃bebe]. However, the learner is required to rerank its constraint hierarchy due to errors introduced by Align-L which only occur with phrases such as [lezami] and [œ̃nami]14 shown in (27). (27) a. /lez/+/bebe/ NoC.C NoV.V Align-L Max [lez.bebe] *! ☞ [le.bebe] * b. /lez/+/ami/ NoC.C NoV.V Align-L Max ☹ [le.zami] *! ☞ [le.ami] *! * At this stage, the input forms /lez/ and /bebe/ directly enter the lexicon of the learner as there are no errors made on them. However, the phrase leading to the error in (27b) are shown in table (28) below. 14 The underlying assumption is that when the three markedness constraints are ranked equally at the top in the initial state, it essentially corresponds to maintaining six different permutations, such as A > B > C, A > C > B, and so forth. In the permutation that features ALIGN-L > NOV.V, learners would be making such errors shown in (27b). 30 (28) Error archive with errors of the CG (NoC.C, NoV.V, Align-L >> Max) Errors by CG Input W ~ L NOC.C NOV.V ALIGN-L MAX  a. L W1: /lez+ami/ le.zami ~ le.ami W L W  b. L W1: /œ̃n+ami/ œ̃.na.mi ~ œ̃.ami W L W As the table in (28) shows, the two markedness constraints that prefer no losers are NOC.C and NOV.V. The biased constraint demotion would result in a crucial ranking among the markedness constraints, so they are no longer equally ranked in the top stratum of the hierarchy in (29). The two errors in (28a‒b) are archived successfully, as the learner proceeds. (29) Liaison G1: NO C.C, NO V.V >> ALIGN-L >> MAX In the second block of learning, learners are presented with the non-liaison morphemes only: {ʒœn+bebe, ʒœn+ami, …, ʒɔli+ami, ʒɔli+bebe, …}, and they would make errors with these new word1s with their current grammar in G1 shown in tableaux below in (30). (30) /ʒœn/+/bebe/ NOC.C NOV.V ALIGN-L MAX ☹ [ʒœn.bebe] *! ☞ [ʒœ.bebe] * /ʒɔli/+/ami/ NOC.C NOV.V ALIGN-L MAX ☹ [ʒɔli.ami] *! ☞ [ʒɔ.lami] * * Due to the errors recorded in their error archive recently as exemplified in the table below in (31), they are required to rerank and update their highest-ranked constraints from G1. Errors (31a‒b) are previous errors from the first block stored in the error archive and errors (31c‒d) are errors made by the current grammar marked by . 31 (31) Error archive with errors of the CG (NO C.C, NO V.V >> ALIGN-L >> MAX) Errors by CG Input W ~ L NOC.C NOV.V ALIGN-L MAX a. L W1: /lez+ami/ le.zami ~ le.ami W L W b. L W1: /œ̃n+ami/ œ̃.na.mi ~ œ̃.ami W L W  c. NL W1: /ʒœn+bebe/ ʒœn.bebe ~ ʒœ.bebe L W  d. NLW1: /ʒɔli+ami/ ʒɔli.ami ~ ʒɔ.lami L W W As the table in (31) shows, no markedness constraint prefers only Ws, therefore the winner-preferring faithfulness constraint MAX is ranked first at the top stratum in (32) and the other constraints are basically demoted. (32) Liaison G2: Max >> No C.C, No V.V, Align-L During the second block, the learners are only exposed to evidence of the non-liaison morphemes. However, the ideal learner not only has a complete archive of the errors, but they also have access to the lexicon they learned in this language up until this point. Even though they do not encounter them in this block, they must notice that the phrases in the second block differ significantly from the earlier phrases to eventually realize that the current G2 grammar will produce errors with /lez+bebe/ and other phrases with a similar structure (...VC.CV…) as demonstrated in a tableau in (33). Recall that these input to these phrases, previously shown in a tableau in (27a), had entered the lexicon directly with no issues in the first block. (33) /lez/+/bebe/ MAX NOC.C NOV.V ALIGN-L ☞ [lez.bebe] * ☹ [le.bebe] *! Now powered by the G2, this recent error initiates an update to the grammar. As the learner compiles all evidence in the archive, they would realize the necessity of addressing the ranking paradox between the morphemes belonging to the two classes of word1s. The table below, which includes all the errors, illustrates the minimal inconsistent pair that highlights the inconsistency (34d vs 34e) in bold—where specific constraints (MAX and NOC.C) exhibit the opposite preferences for the morphemes presented in the two blocks of the experiment. The learner is unable to continue the reranking process to install any constraints at this point. 32 (34) Error archive with errors of the CG (Max >> No C.C, No V.V, Align-L) Errors by CG Input W ~ L MAX NO C.C NO V.V ALIGN-L a. LW1: /lez+ami/ le.zami ~ le.ami W W L b. LW1: /œ̃n+ami/ œ̃.na.mi ~ œ̃.ami W W L c. NLW1: /ʒɔli+ami/ ʒɔli.ami ~ ʒɔ.lami W L W d. NLW1: /ʒœn+bebe/ ʒœn.bebe ~ ʒœ.bebe W L  e. LW1: /lez+bebe/ le.bebe ~ lez.bebe L W  f. LW1: /œ̃n+bebe/ œ̃.bebe ~ œ̃n.bebe L W Following the instruction in (17) to “clone the constraint that prefers Ws in all instances of the errors committed by the current grammar and index it to morphemes for which it prefers only Ws for those errors”, the learners can activate their bias favouring the errors made by the current grammar marked by  when resolving the inconsistency. Therefore, they would clone the relevant constraint that prefers Ws for the errors made by the current grammar (NOC.C-L) indexed to those morphemes /lez/ and /œ̃n/ as shown in (34). With the addition of the new constraint, now there is a constraint that prefers only Ws with no inconsistencies (NOC.C-L), therefore that constraint(s) is ranked at the top stratum. After that, the errors (34e‒f) are successfully resolved and the reranking can proceed as usual resulting in the final grammar below in (35). (35) Liaison G2.2: NO C.C-L2**, NO C.C-L1* >> MAX >> NOC.C, ALIGN-L, NOV.V *L1: {/lez/}, **L2: {/œ̃n/} Eventually the learner then merges the two No C.C-L constraints under one constraint in the final grammar as shown in (36). (36) Liaison Final G: No C.C-L* >> Max >> No C.C, No V.V, Align-L15 *L: {/lez/, /œ̃n/} 15 Recall that other faithfulness constraints such as DEP are not shown in this hierarchy due to reasons of space but it is at the same stratum as MAX, outranking NOV.V. 33 2.5.2. Ordered learning trajectory - Non-liaison first In this group of learners, the first part involves receiving two non-liaison morphemes while the second part includes the two liaison morphemes. In this manner, the initial evidence presented to learners based on what they encounter in the first block lacks any form of inconsistency. In the first block, learners encounter evidence of the following set of non-liaison phrases: {ʒœn+bebe, ʒœn+ami, … & ʒɔli+ami, ʒɔli+bebe, …}. Since the learning data does not contain alternations, the ideal learner is essentially only required to perform lexicon optimization and store underlying representations which are identical to the output. By the end of the first block, assuming an initial state bias from G0, the learner does make errors with examples such as [ʒœnbebe] or [ʒɔliami]16 shown in (37). (37) a. /ʒœn/+/bebe/ NOC.C NOV.V ALIGN-L MAX ☹ [ʒœn.bebe] *! ☞ [ʒœ.bebe] * b. /ʒɔli/+/ami/ NOC.C NOV.V ALIGN-L MAX ☹ [ʒɔli.ami] *! ☞ [ʒɔ.lami] *! * Based on the recent errors present in their error archive as exemplified in the table below in (38), they are required to rerank and update their highest-ranked constraints from the initial state in G0. (38) Error archive with errors of the CG (NoC.C, NoV.V, Align-L >> Max) Errors by CG Input W ~ L NOC.C NOV.V ALIGN-L MAX  a. NLW1: /ʒɔli+ami/ ʒɔli.ami ~ ʒɔ.lami L W W  b. NL W1: /ʒœn+ami/ ʒœ.na.mi ~ ʒœ.ami W L W  c. NL W1: /ʒœn+bebe/ ʒœn.bebe ~ ʒœ.bebe L W 16 Same as the previous footnote, when the three markedness constraints are ranked equally at the top in the initial state, it essentially corresponds to maintaining six different permutations, such as A > B > C, A > C > B, and so forth. In the permutation that features NOV.V>>ALIGN-L, ultimately learners would be making such errors as shown in (36b). 34 Due to the fact that both types of marked structures (V.V and C.C) as well as syllable misalignments are allowed in the output and the inputs remain the same in their outputs without any alternations, a reversal of the faithfulness and markedness constraints in the constraint hierarchy is bound to occur. Hence, the learner starting from G0, must update its grammar with a biased constraint demotion algorithm and in doing so all markedness constraints must be installed after Max, since none of them exclusively prefer Ws as shown in G1 (39). (39) Non-liaison G1: Max >> No C.C, No V.V, Align-L In the second block of their learning, they are presented with the liaison morphemes only: {le+bebe, lez+ami, …, œ̃+bebe, œ̃n+ami, …}. It is crucial that the ideal learner establishes the semantic connection between the allomorphs and identifies the larger consonant-final allomorph /lez/ and /œ̃n/ as the underlying representation employing the heuristic that we introduced in section 2.4.2. Such a learner relying on a uniform input of /lez/ would make errors on phrases such as [lebebe] or [œ̃bebe] following the previous grammar in G1, shown in (40). (40) /lez/+/bebe/ MAX NOC.C NOV.V ALIGN-L ☞ [lez.bebe] * ☹ [le.bebe] *! /œ̃n/+/bebe/ MAX NOC.C NOV.V ALIGN-L ☞ [œ̃n.bebe] * ☹ [œ̃.bebe] *! These recent errors need to be present in the error archive. As the learners compile all evidence in the archive, they realize the necessity of addressing the ranking paradox between the morphemes belonging to the two classes of word1s. The table below, which includes all the errors, illustrates the minimal inconsistent pair that highlights the inconsistency (41c vs 41e) in bold—where the specific constraints (MAX and NOC.C) exhibit the opposite preferences for the morphemes presented in the two blocks of the experiment. The learner is unable to continue the reranking process and to install any constraints at this juncture. 35 (41) Error archive with errors of the CG (MAX >> NO C.C, NO V.V, ALIGN-L) Errors by CG Input W ~ L MAX NOC.C NOV.V ALIGN-L a. NLW1: /ʒɔli+ami/ ʒɔli.ami ~ ʒɔ.lami W L W b. NL W1: /ʒœn+ami/ ʒœ.na.mi ~ ʒœ.ami W W L c. NL W1: /ʒœn+bebe/ ʒœn.bebe ~ ʒœ.bebe W L  d. L W1: /lez+bebe/ le.bebe ~ lez.bebe L W  e. L W1: /œ̃n+bebe/ œ̃.bebe ~ œ̃n.bebe L W Similar to the previous scenario, following the instruction in (17) the learners can take advantage of their bias favouring the errors made by the current grammar marked by  when resolving the inconsistency. Therefore, they would clone the relevant constraint that prefers Ws for the errors made by the current grammar (NOC.C-L) indexed to those morphemes /lez/ and /œ̃n/. As shown in (42) NOC.C-L is the only markedness constraint that prefers only Ws, therefore, it is ranked at the top. After that, the errors (d-e) are resolved and the reranking can proceed as usual resulting in the final grammar below in G2. (42) Non-liaison G2: NOC.C-L2**, NOC.C-L1* >> MAX >> NOC.C, ALIGN-L, NOV.V *L1: {/lez/}, **L2: {/œ̃n/} Eventually the learner then merges the two NOC.C-L constraints under one constraint in the final grammar as shown in (43). (43) Non-liaison Final G: NOC.C-L* >> MAX >> NOC.C, NOV.V, ALIGN-L *L: {/lez/, /œ̃n/} 2.5.3. Mixed Learning trajectory For this group of learners, the learning data of the 2 morpheme types is not presented in an isolated manner, rather they see both types of morphemes at the same time: one liaison morpheme and one non-liaison morpheme. In this manner, the first type of evidence presented to learners based on what they encounter in the first block, would in fact present an inconsistency to learners. In the first block, learners encounter evidence of the following set of liaison and non-liaison phrases: {le+bebe, lez+ami, … & ʒœn+bebe, ʒœn+ami, …}. The learner's task is slightly different in nature here. An ideal learner needs to first recognize the crucial difference between 36 these two morphemes, namely that one of them lacks a stable output form and exhibits an alternation. The representations of non-liaison morphemes can be learned through lexicon optimization. However, once the learner identifies that one of the morphemes is special in that it has two output forms with some established semantic connection, they need to employ the proposed heuristic to maximize the structure in the input. Thus, they determine the larger allomorph /lez/ to be the underlying representation. Phrases such as [lebebe] and [lezami] do not cause errors at first. However, by the end of the first block, assuming an initial state bias from G0, the learner does make errors with examples such as [ʒœnbebe] or [ʒœnami]17 show in tableaux in (44). (44) a. /ʒœn/+/bebe/ NOC.C NOV.V ALIGN-L MAX ☹ [ʒœn.bebe] *! ☞ [ʒœ.bebe] * b. /ʒœn/+/ami/ NOC.C NOV.V ALIGN-L MAX ☹ [ʒœn.ami] *! ☞ [ʒœ.ami] *! * At this stage, the input forms such as /lez/ and /bebe/ and /ami/ directly enter the lexicon of the learner as there are no errors made on them. However, the phrase leading to the error in (44) has to be moved to the error archive as shown in table (45) below. Now, based on the recent errors present in their error archive marked by  they are required to rerank and update their highest-ranked constraints from the initial state in G0. (45) Error archive with errors of the CG (NoC.C, NoV.V, Align-L >> Max) Errors by CG Input W ~ L NO C.C NO V.V ALIGN-L MAX  a. NLW1: /ʒœn+bebe/ ʒœn.bebe ~ ʒœ.bebe L W  b. NLW1: /ʒœn+ami/ ʒœ.nami ~ ʒœ.ami W L W Due to the fact that marked structures including C.C are allowed, the relevant markedness constraint is preferred by Ls. The biased constraint demotion would initiate the reranking of initial 17 Same as the previous footnotes, when the three markedness constraints are ranked equally at the top in the initial state, in the permutation that features ALIGN-L >> NOV.V, ultimately learners would be making such errors as shown in (43b). 37 state markedness constraints outranking other constraints at the top. Consequently, among the possible markedness constraints, the learner must install No V.V as the only markedness constraint that prefers only Ws once the relevant row of error in (45b) is resolved shown in (46). (46) Error archive with errors of the CG (NoC.C, NoV.V, Align-L >> Max) Errors by CG Input W ~ L NO C.C NO V.V ALIGN-L MAX  a. NLW1: /ʒœn+bebe/ ʒœn.bebe ~ ʒœ.bebe L W  b. NLW1: /ʒœn+ami/ ʒœ.nami ~ ʒœ.ami W L W As the rest of the reranking algorithm continues based on (46a), the next markedness constraint that prefers no losers is Align-L, therefore it is placed in the second stratum which outranks Max. The final step installs NoC.C at the bottom as it prefers Ls as shown in G1 (47). (47) Mix G1: NO V.V >> ALIGN-L >> MAX >> NO C.C Once the learners form the hierarchy in G1, they would immediately make errors with the phrases including the other word1 in this block, which is a liaison word1, shown in a tableau in (48) such as [lebebe]. (48) /lez/+/bebe/ NOV.V ALIGN-L MAX NOC.C ☞ [lez.bebe] * ☹ [le.bebe] *! This recent error needs to be recorded in the error archive shown in (49c). As the learners compile all evidence from errors they learned from in this block, they realize the necessity of addressing the ranking paradox between the morphemes belonging to the two word1s they encountered in this block. The table below in (49), illustrates the minimal inconsistent pair that highlights the inconsistency (49b vs 49c) in bold. The learner is unable to continue the reranking process and to install any constraints. 38 (49) Error archive with errors of the CG (NO V.V >> ALIGN-L >> MAX >> NO C.C) Errors by CG Input W ~ L NO V.V ALIGN-L MAX NO C.C a. NL W1: /ʒœn+ami/ ʒœ.nami ~ ʒœ.ami W L W b. NL W1: /ʒœn+bebe/ ʒœn.bebe ~ ʒœ.bebe W L  c. L W1: /lez+bebe/ le.bebe ~ lez.bebe L W In the event of detecting an inconsistency among constraints’ Ws and Ls, following the instruction in (17) the learners can take advantage of their bias favouring the errors made by the current grammar to resolving the inconsistency. Therefore, they would clone the relevant constraint that prefers Ws for the errors made by the current grammar indexed to that morpheme /lez/ (NO C.C-L). The new added constraint, NOC.C-L, is the only markedness constraint that prefers only Ws. Therefore, according to the biased constraint demotion algorithm it is ranked at the top stratum. After the error (49c) is resolved, the reranking can proceed as usual (similar to the steps 45‒47) resulting in the grammar G1.2 below in (50). (50) Mix G1.2: No C.C-L* >> No V.V >> Align-L >> Max >> No C.C *L: {/lez/} In the second block of the experiment, participants encounter the other liaison and non-liaison morphemes: {œ̃+bebe, œ̃n+ami, … & ʒɔli +ami, ʒɔli +bebe, …}. This block shares some similarities with the first block but also presents some new challenges. Similar to before, they must distinguish the inconsistency between the new liaison word1s from the new non-liaison word1s. For the liaison word1s, the ideal learner must connect the two allomorphs semantically and identify the larger allomorph as the underlying representation. The novelty in this block of the experiment goes beyond simply recognizing the inconsistencies within the grammar. It also involves the learners' ability to classify the new liaison word alongside /lez/ and the new non-liaison words with /ʒɔli/. However, the learners begin this block by making errors with /ʒɔli/18, as the NOV.V constraint is highly ranked in G1.2 shown in the tableau in (51). 18 This order of errors is specific to this version. There are in fact two versions of the unordered group in the experiment to counterbalance the effect of specific errors. The other version of this trajectory would be to receive /ʒɔli/ in the first block and /ʒœn/ in the second block. This difference does not affect how many stages of G there would be overall, but it is worth mentioning that the other version not reviewed here leads to a different error at this point with [ʒœnbebe]. 39 (51) /ʒɔli/+/ami/ NOC.C-L NOV.V ALIGN-L MAX NOC.C ☞ [ʒɔli.ami] *! ☹ [ʒɔ.lami] * * This recent error (51) needs to be present in the error archive, as shown in (52d). Once this new error is recorded, the learner is required to rerank and update their constraint hierarchy from the previous grammar. (52) Error archive with errors of the CG (No C.C-L* >> No V.V >> Align-L >> Max >> No C.C) Errors by CG Input W ~ L No C.C-L No C.C No V.V Align-L Max a. NL W1: /ʒœn+ami/ ʒœ.nami ~ ʒœ.ami W L W b. NL W1: /ʒœn+bebe/ ʒœn.bebe ~ ʒœ.bebe L W c. L W1: /lez+bebe/ le.bebe ~ lez.bebe W W L  d. NLW1: /ʒɔli+ami/ ʒɔli.ami ~ ʒɔ.lami L W W According to the biased constraint demotion algorithm, No C.C-L is still ranked at the top stratum since it is the only constraint that prefers only Ws. No other markedness constraints prefer only Ws, therefore Max outranks them as the grammar G2 below shows in (53). (53) Mix G2: NO C.C* >> MAX >> NO C.C, ALIGN-L, NO V.V *L: {/lez/} Importantly, for this particular learner, the highest ranked NOC.C-L constraint is only associated with /lez/. Consequently, leading the learner to initially make errors when confronted with the new liaison word /œ̃n/ as shown in a tableau in (54). (54) /œ̃n/+/bebe/ NOC.C-L MAX NOC.C NOV.V ALIGN-L ☞ [œ̃n.bebe] * ☹ [œ̃.bebe] *! 40 This recent error (54) needs to be recorded in the error archive shown in (55e). Similar to the other errors previously, once this new error is added to the error archive, they are required to update their constraint hierarchy. (55) Error archive with errors of the CG (NO C.C* >> MAX >> NO C.C, ALIGN-L, NO V.V) Errors by CG Input W ~ L No C.C-L Max No C.C No V.V Align-L a. NLW1: /ʒœn+ami/ ʒœna.mi ~ ʒœ.ami W W L b. NLW1: /ʒœn+bebe/ ʒœn.bebe ~ ʒœ.bebe W L c. LW1: /lez+bebe/ le.bebe ~ lez.bebe W L W d. NLW1: /ʒɔli+ami/ ʒɔli.ami ~ ʒɔ.lami W L W  e. LW1: /œ̃n+bebe/ œ̃.bebe ~ œ̃n.bebe L W The learner is unable to continue the reranking procedure as the errors in (54b vs 54e) are in conflict and there are no constraints that prefer only Ws. At this juncture, following the instruction in (17) their errors made by the current grammar can bias the learners when resolving the inconsistency. Therefore, they would clone the relevant constraint that prefers Ws for the errors made by the current grammar indexed to that morpheme /œ̃n/ (No C.C-L). This results in two cloned constraints as it is shown in the hierarchy below in (56). (56) Mix G2.2: NOC.C-L2**, NOC.C-L1* >> MAX >> NOC.C, ALIGN-L, NOV.V *L1: {/lez/}, **L2: {/œ̃n/} However, it is expected that in such a situation these cloned constraints would merge; resulting in a single constraint being indexed to both morphemes instead as shown below in the final grammar in (57): (57) Mix final G: NOC.C-L* >> MAX >> NOC.C, ALIGN-L, NOV.V *L: {/lez/, /œ̃n/} 2.5.4. Predicted outcomes of trajectories In this subsection, the predicted outcomes of the hypothesized trajectories are outlined. First, a summary of the trajectory of ideal learners who learned the artificial language through three different ordering of learning data is shown in the following Table 2-1. The three groups have the 41 same initial state (G0) and end state (GE), but they differ in the order of learning data and thus also in their trajectories shaped in the two blocks. The constraint hierarchies built in the first block are shown as G1 and the constraint hierarchies build in the second block are shown as G2. If a block has more than one constraint hierarchy they are separated by a dashed line for clarity. There are several aspects in which these ideal learners can be evaluated on, including: a. underlying representations, b. reranking of the constraint hierarchy, c. lexicon indexation, and d. constraint cloning. In the following subsection on predictions, I will review the theoretical pressures pertaining to an ideal learner for each aspect individually. It is important to note that the cognitive and memory constraints associated with each of these trajectories could impact learners’ performance in various ways in experimental settings, a topic I will address under the pressures faced by a suboptimal learner in the last subsection. In the experiment, after being presented with the learning data, participants engage in a series of forced choice tasks. The tasks are comparable to selecting between pairs of winning and losing candidates. By quantifying their accuracy with forced-choice tasks, making inferences about their learning is also possible through analyzing their errors. The main research question targets the difficulty of learning morpheme-specific alternations along certain theoretical dimensions which are included in a theory of learning within OT. Given that the only manipulation for these groups of participants is the distribution and order of learning input, I hypothesize that there will be differences in the difficulty of learning which would lead to differential learning outcomes in two respects simultaneously: quantitatively, and qualitatively, that is, in terms of overall differences across the groups, and the distribution of errors within each group, respectively. 42 Table 2-1. The summary of learning trajectories of the three groups of learners Liaison First Non-liaison First Mixed Initial state (G0) No C.C, No V.V, Align-L >> Max No C.C, No V.V, Align-L >> Max No C.C, No V.V, Align-L >> Max Block1 (G1) No C.C, No V.V >> Align-L >> Max Max >> No C.C, No V.V, Align-L No V.V >> Align-L >> Max >> No C.C ---------------------------------------- No C.C-L* >> No V.V >> Align-L >> Max >> No C.C *L: {/lez/} Block2 (G2) Max >> No C.C, No V.V, Align-L ---------------------------------------- No C.C-L**, No C.C-L* >> Max >> No C.C, No V.V, Align-L **L: {/œ̃n/} *L: {/lez/} No C.C-L**, No C.C-L* >> Max >> No C.C, No V.V, Align-L **L: {/œ̃n/} *L: {/lez/} No C.C-L* >> Max >> No C.C, No V.V, Align-L *L: {/lez/} ----------------------------------------- No C.C-L**, No C.C-L* >> Max >> No C.C, No V.V, Align-L **L: {/œ̃n/} *L: {/lez/} End state (GE) No C.C-L* >> Max >> No C.C, No V.V, Align-L *L: {/lez/, /œ̃n/} No C.C-L* >> Max >> No C.C, No V.V, Align-L *L: {/lez/, /œ̃n/} No C.C-L* >> Max >> No C.C, No V.V, Align-L *L: {/lez/, /œ̃n/} 43 2.5.4.1. Predictions for an optimal learner a. Underlying representations in alternations The ideal learning of morpho-phonological patterns begins with the creation of underlying representations for new morphemes. In the experiment, all learners must understand that two of the four morphemes, described as liaison morphemes, share a single input corresponding to two output variants. Then they can posit the correct underlying representation using the heuristic. The rationale is that if the type of data and the order in which learning data is presented influences the learning of the underlying representations of alternations, there would be differences among the groups’ accuracy reflective of that. Specifically, learners who follow the liaison-first trajectory face less challenges to compute the underlying representations of the allomorphs. This is because the initial evidence of both liaison morphemes they receive in the first block will facilitate their understanding of the 2-1 mapping from output to input, rather than relying on secondary or inconsistent evidence. Conversely, learners in the non-liaison-first trajectory would find it more challenging, because they lost the clear opportunity in the very beginning to learn about the phonologically motivated alternations in the mini-language. This might hinder their ability to notice the alternations and thereby establish a unified input through the heuristic. The unordered group, on the other hand, has access to only one liaison morpheme learning data compared to the liaison-first group in the first block, placing them in an intermediate difficulty position. Therefore, this rationale for learning the underlying representation predicts the following order of learning difficulty among the groups, from easiest to hardest: liaison-first > unordered > non-liaison-first b. Reranking of the constraint hierarchy During the morpho-phonological learning process driven by errors, once a learner has explored the possible underlying representations and selected the appropriate one, the next step involves reranking the constraints until reaching a final state grammar without errors. The rationale is that if the order in which learning data is presented influences the trajectory and steps of constraint reranking, the differences in performance across the groups would reflect that. In principle, the hypothesis is that having fewer stages of reranking is easier. That means, learners following a non-liaison-first trajectory are expected to find it easier to converge on the end state grammar. This is because they only need to update and rerank their constraint hierarchy twice to arrive at the correct end state grammar, whereas other groups require more reranking stages. Therefore, this rationale about reaching the end state grammar predicts the following order of learning among the groups from easiest to hardest: non-liaison-first > liaison-first > unordered 44 c. Lexicon indexation and constraint cloning The next crucial aspect of learning morpheme-specific alternations involves identifying inconsistencies in the grammar and acknowledging that certain morphemes within a subset of the lexicon may conflict with their current ranking. I predict that in scenarios requiring inconsistency detection, if the process of learning lexicon indexation varies depending on the order and type of learning data presented, the differences in performance among groups would be reflective of that. Specifically, the hypothesis is that it is easier for learners to recognize that a group of morphemes must be indexed to specific constraints when they are exposed to multiple morphemes of the same class in each block. Consequently, the two ordered groups would find it easier to choose indexations compared to the unordered group. The unordered group, in contrast, must learn that some morphemes require indexing twice, in the first and second blocks of the experiment. Furthermore, learners need to determine which constraints to clone and index to a subset of the lexicon. Echoing the previous argument on lexicon indexation, I predict that recognizing when a constraint needs to be cloned and indexed is more straightforward when learners encounter the set of morphemes in a class together. Moreover, this expectation also arises from the fact that the ordered groups can integrate their cloned versions of the constraints for each instance of the liaison morphemes as they generate them simultaneously, while the unordered group must grapple with this decision once more later as they have cloned their constraints in two separate blocks. Therefore, this rationale for constraint cloning and lexicon indexation predicts the following order of learning among the groups from easiest to hardest: non-liaison-first, liaison-first > unordered d. Distribution of errors within each group I also predict that the learning and performance of the three groups would differ qualitatively with each other, namely with respect to the type of errors that they frequently make. If the difficulties of learning are not of the same nature for the three groups, their error patterns will show differences in learning. Specifically, each group will make less errors with the type of phrases presented to them in their first block compared to the second block. Therefore, if the order of receiving the input affects their learning, it is easier to learn liaison phrases for the liaison-first group compared to the other groups and it is easier to learn non-liaison phrases for the non-liaison-first group compared to the other groups. 2.5.4.2. Predictions for a suboptimal learner There are various ways in which in an experimental setting the learner might face extra limitations due to memory or cognitive load of the tasks. The first issue could be influenced by restraints on 45 memory and its connection to the storage of the lexicon and the error archive. For instance, during block two of the experiment, the liaison-first group has to recall from memory that certain inputs that were learned in the first block without any errors, would lead to errors with their updated grammar at that stage. In this scenario, a suboptimal learner in an experimental setting might find it more difficult to hold the words and phrases in the language in memory for a longer time to consider their errors and non-errors as they progress in the experiment towards the end. This rationale for possible memory constraints leads to the predictions that the difficulty among groups ranked from easiest to hardest are as follows: non-liaison-first > liaison-first, unordered Another cognitively challenging aspect of learning concerns the cost of learning generalizations and lexical optimization sequentially. If a learner has to learn morpheme-specific alternations in an inconsistent grammar, they must learn two things: a) simple phonologically-motivated generalization supported by a universal bias towards unmarked structures and b) more complicated lexical facts. Hsu and Chater (2010) propose a simplicity-based cognitive model for the logical problem of language acquisition where there is a trade-off in the costs of learning a simple generalization with less data and learning lexical and more complicated rules with more data. Inspired by the ideas in the simplicity framework, I hypothesize that cost of learning from an inconsistent set of learning data in the direction which the learner retreats from a generalization to lexicon optimization through receiving more evidence would be lower than learning in the opposite direction, from lexicon optimization to a generalization about alternations. Consequently, this rationale about the cognitive costs of the learning trajectory predicts the following order of difficulty among the groups from easiest to hardest: liaison-first > non-liaison-first, unordered. Table 2-2. The summary of predictions of difficulty of learning by different aspects easiest hardest UR of alternations liaison-1st > unordered > non-liaison-1st Reranking of the constraint hierarchy non-liaison-1st > liaison-1st > unordered Lexicon indexation + constraint cloning liaison-1st, non-liaison-1st > unordered Learning liaison patterns liaison-1st > non-liaison-1st, unordered Learning non-liaison patterns non-liaison-1st > liaison-1st, unordered memory constraints non-liaison-1st > liaison-1st, unordered cognitive costs liaison-1st > non-liaison-1st, unordered 46 To summarize the predictions in this subsection, Table 2-2 shows the different groups ranked in the order of difficulty for each prediction. The predictions about the difficulty of learning with respects to various aspects could be evaluated by examining the performance differences among the three groups during testing. In the next chapter, the experimental design, material, and training and testing procedures are described in more detail. 47 Chapter 3 Methods 3. Methods 3.1. Participants A total of 241 participants were recruited from the UBC linguistics participants pool in the Alternating 1st, Non-alternating 1st, and Mixed experimental conditions with 82, 83, and 76 participants, respectively. This convenience sample consisted of participants aged 16 to 49 (Mean=20.6, SD = 4), with 167 as female (69%), 49 participants as male (21%) and 25 (10%) as nonbinary or unreported. Regarding the language background, 211 reported English as their dominant language, and 30 individuals listed English as their non-dominant language. Among the non-English dominant languages, Mandarin and/or Cantonese (13), Korean (5), Japanese (4), and Tagalog (3) were listed. Due to not meeting the language background eligibility criterion of the study, 5 French-speaking participants were excluded, specifically as they were raised with Francophone caretakers with an age of acquisition of French below four. More information about the data collection procedures and the inclusion and exclusion criteria is provided in Section 3.5. 3.2. Overview of design The experimental design employed a between-subjects approach, consisting of three distinct conditions. The conditions varied only in the distribution order and the content of the training blocks, but all participants completed the training phase with the same set of items and the same number of training trials by the time they reached the testing phase. Consequently, this independent variable was categorical, consisting of three levels (i.e., the training conditions). The dependent variable was binary, representing participants’ correct responses in two forced-choice tasks during testing. Below is a diagram that provides a step-by-step overview of the experimental design in Figure 3-1. 48 The experiment was conducted remotely (online) via a web browser. Participants had to blindly register in only one the conditions to receive a link. After the landing page, participants were required to complete a consent form and undergo a headphone check with six trials. Correct answers to four and more trials allowed them to progress to the experiment. Introductory instructions about the artificial language were provided to participants at the outset of the experiment and more specific instructions before the training and testing tasks. The training phase included 144 trials, and the testing phase included 64 trials overall. At the end of the experiment, an optional debriefing form was made available, allowing participants to offer written feedback regarding their approach to the experiment. Further details about the procedure in each phase and the types of trials will be discussed in Section 3.4 after reviewing the materials used in the experiment in Section 3.3. 3.3. Materials All the nonce-word stimuli used throughout the training phase of the experiment consisted of two-word phrases (word1 + word2) presented to participants as audio stimuli and simultaneously accompanied by visual stimuli. In the introduction to the mini-language that participants received, these phrases were framed as possessive phrases in an alien language, where the first word is the possessor and the second word is the possessed item (mirroring the most common order in English). These items were described as various everyday items that the aliens brought in their luggage to Earth to disguise themselves on their tour of the galaxy. The contextual scenario was introduced to participants as an opportunity to learn about possessive phrases in that alien language. 3.3.1. Training and testing Stimuli In total, there were four word1 stimuli, representing the aliens' names, categorized into alternating and non-alternating types. Each alternating word1 had two allomorph forms. The phonological conditioning pattern of the alternating word1s was analogous to that of the liaison allomorphs in French. The C-final allomorph ([meʃ] or [dit]) would occur before V-initial word2s and the V-final allomorph ([me] or [di]) would occur before C-initial word2s. The consonants in bold letters Consent formHeadphone checkInstructionsTraining phaseTesting phaseFeedbackFigure 3-1. Step-by-step overview of the experimental design and procedure 49 /ʃ/ and /t/ are referred to as the liaison consonant (LC). Table 3-1 below displays all the word1s designed to be analogous to the morpheme-specific alternations in French, as presented in Section 2.2 in Examples (1−5). Table 3-1. Word1 stimuli representing alien names Alternating word1s Non-alternating word1s V(C)-final C-final V-final [me], [meʃ] [di], [dit] [kɑn] [lu] (as in petit) (as in jeune) (as in joli) The rest of the stimuli were 32 word2s which were constructed using 18 consonants (/p b t d k g tʃ dʒ f v s z ʃ n m r l j/) and six vowels (/i e u o æ ɑ/) organized into four distinct word shapes: V.CVC, V.CV, CV.CVC, and CV.CV. The segments adhered to the phonemic inventory and phonotactic rules of English so the vowels /e/ and /o/ were phonetically [eɪ] and [oʊ], except before /r/. Each vowel appeared between 4 and 6 times, while each consonant was included between 2 and 4 times in the overall list of word2s. Efforts were made to counterbalance the position of vowels and consonants in the words as much as possible. Table 3-2 below categorizes the word2s into V-initial and C-initial types. Sixteen of the word2 stimuli appeared both in training and in testing tasks 1 and 2, while the other 16 were only used in task 3 in testing (i.e., they did not appear in training). Table 3-2. Word2 stimuli representing everyday object nouns V-initial word2s C-initial word2s V.CVC V.CV CV.CVC CV.CV Training, testing task 1 and task 2 /edæp/ /æte/ /pæzɑm/ /vezu/ /ibud/ /ogi/ /budol/ /mæti/ /ɑtæl/ /ufe/ /gɑbiʃ/ /kisɑ/ /ugæʃ/ /ido/ /dʒomet/ /peku/ Testing task 3 (novel) /itʃæn/ /ezɑ/ /færus/ /fule/ /ɑjor/ /ɑvi/ /tʃægef/ /sædʒɑ/ /okɑn/ /osu/ /runip/ /rejɑ/ /eʃin/ /imɑ/ /zoʃek/ /voli/ The word1 and training word2 stimuli paired together would result in two-word phrases that constitute the items in the training trials, as well as the choice stimuli in testing task 1 and the 50 prompt stimuli in the testing task 2 trials. The word1 and novel word2 stimuli paired together would result in two-word phrases that are used only as the prompt stimuli in the testing task 3. Further details about the distribution of the stimuli in the training and testing phase are provided in Section 3.4 along with the experimental procedure. 3.3.2. Audio stimuli The audio stimuli were recorded by a phonetically-trained female speaker of Canadian English in a controlled recording environment, using a Shure WH20 dynamic headset microphone and PreSonus Studio One Pro software with a sampling rate of 44.1 kHz and a bit depth of 32-bit. All audio files were adjusted and normalized to an amplitude of 50 dB. The phrasal stimuli comprised a list of trisyllabic word1 + word2 phrases structured in six various shapes: CV.CV.CV(C) or CVC.CV.CV(C) or CV.VCV(C). The first vowel was pronounced with an unreduced quality to make sure all the stimuli adhere to the perceived stress pattern ˌσ.ˈσ.σ. The phrasal trisyllabic stimuli were recorded without a carrier phrase, in a list, but the single isolated words, used in testing tasks 2 and 3, were placed within the carrier phrase “I said [target word] again/twice”. The long recordings were transcribed by the researcher and subsequently annotated using the Montreal Forced Aligner 2 package in Python (McAuliffe et al., 2017). Following a thorough review of the annotation text grids produced by the MFA, smaller audio files containing only the target words (ranging from 1 to 3 seconds) were automatically extracted using a script in Praat 6.1.42 (Boersma and Weenink, 2021). 3.3.3. Visual stimuli Each word in the experiment was associated with a distinct and colourful image consistently for all participants. The visual stimuli included 2D vector illustrations of various alien characters and everyday objects, covering themes related to school, the workplace, kitchen items, and more. These illustrations were sourced freely from a vector image and graphics website found on the internet.19 The images were displayed centrally on the screen, with dimensions between a maximum of 580 pixels and a minimum of 256 pixels. Figure 3-2 below provides an example of the illustrations used for the four alien characters and a set of the images of the objects which were the visual stimuli used across all trial types. 19 https://graphicsurf.com/ 51 3.4. Experimental procedure 3.4.1. Training The initial phase of the experiment was dedicated to training participants on the two-word phrases. During this phase, participants listened to a phrase and simultaneously viewed two corresponding images in each trial, similar to the example shown in Figure 3-3. This was a self-paced exposure task, allowing participants to press a key when they felt prepared to advance to the next trial. The training phase included 144 trials and the total duration of this phase was on average 8 (SD=7) minutes for all participants. Figure 3-2. Visual stimuli used for word1 and a sample of visual stimuli used for word2 52 Participants in all three conditions were exposed to the same training stimuli over the course of the training phase; the only difference between the conditions was the distribution order of the training items. All the training trials were organized into 2 blocks. The three conditions are named based on the name of the first block, that is “Alternating 1st” (Alt1st), “Non-alternating 1st” (NonAlt1st) and “Mix” (Mixed). Table 3-3 below illustrates the order of the blocks and trial types for each condition with some examples. For example, in the Alt1st condition: block1 contained phrases constructed with alternating word1s [meʃ]/[me] and [dit]/[di], each combined with 12 word2s, such as: [dit] + /edæp/, [di] + /budol/, [meʃ] + /edæp/, [me] + /kisɑ/ and block2 contained phrases constructed with non-alternating word1s /lu/ and /kɑn/, each combined with 12 word2s, such as: /lu/ + /edæp/, /lu/ + /budol/, /kɑn/ + /edæp/, /kɑn/ + /kisɑ/. Conversely, in the NonAlt1st condition, block 1 included phrases with two non-alternating word1s, and block 2 contained phrases with two alternating word1s. The third condition, Mix, did not consist of phrases exclusively constructed with non-alternating or alternating word1s; rather, each block contained an equal distribution, with half of the phrases created using one alternating word1 and the other half using one non-alternating word1. We recruited participants in two sub-conditions with both orders to counterbalance the effect of order (Mix1: block1 – block2, Mix2: block2 – block1) and later collapsed them into one condition for the analysis. In each block, participants were presented with 24 unique training trials per block. The four word1s were divided equally between the blocks as shown with examples in Table 3-3, two of the Figure 3-3. A sample page of all experimental trials in the web browser 53 word1s appeared in the first block and the other two appeared in the second block. For all conditions, out of the 16 unique word2s half were paired with both word1s while the remaining 8 were limited-context word2s and appeared with only one. In the subsequent tables (and in the next subsection about testing), this distinction among the phrases containing different word2 types is referred to as limited-context versus full-context. For instance, /edæp/ is paired with both word1s inside a block so it is a full-context word2 and /budol/ or /kisɑ/ are paired with just one word1 inside a block so they are limited-context word2s. Therefore, in each block, the 24 training trials consisted of 2 word1s × 8 full-context word2s + 1 word1 × 4 limited-context word2s + 1 word1 × 4 limited-context word2s. This 24-trial list was repeated three times, each time with a different random order, resulting in a total of 72 training trials per block (24 trials × 3 repetitions). As there were two blocks, the training phase consisted of 144 trials overall. A pseudo-randomization order was employed to ensure that the word1 + full-context word2 phrases (that shared the same word2 but differed in their word1) were immediately adjacent to each other in the list of 24 trials. Consequently, the special arrangement of the 16 word2s in the entire training phase allowed participants to encounter half of the word2s in full contexts paired with 4 unique word1s while also being exposed to half of the word2s in a limited context, once with an alternating word1 and once with a non-alternating word1. For a comprehensive list of stimuli in each block, please refer to the Appendix A. 54 Table 3-3. Structure and the content of the blocks in the training phase of the experiment Alternating 1st Condition Non-alternating 1st Condition Mixed Condition Training block 1 word2 type “alternating word1” “non-alternating word1” “non-alternating/ alternating word1” n total 72=24×3 full-context limited-context full-context limited-context [dit] + /edæp/ [di] + /budol/ … [meʃ] + /edæp/ [me] + /kisɑ/ … /lu/ + /edæp/ /lu/ + /pæzɑm/ … /kɑn/ + /edæp/ /kɑn/ + /vezu/ … /lu/ + /edæp/ /lu/ + /pæzɑm/ … [meʃ] + /edæp/ [me] + /kisɑ/ … Training block 2 “non-alternating word1” “alternating word1” “non-alternating / alternating word1” n total 72=24×3 full-context limited-context full-context limited-context /lu/ + /edæp/ /lu/ + /pæzɑm/ … /kɑn/ + /edæp/ /kɑn/ + /vezu/ … [dit] + /edæp/ [di] + /budol/ … [meʃ] + /edæp/ [me] + /kisɑ/ … /kɑn/ + /edæp/ /kɑn/ + /vezu/ … [dit] + /edæp/ [di] + /budol/ … Table 3-4 below illustrates the structure inside each block for the specific pseudo-randomization order of training trials which applies to all conditions. For instance, when the full-context word2 /edæp/ appears in the presentation list, we ensured that it also appears in the next phrase that follows. In an exclusively alternating word1 block, the sequence of phrases would be [dit] + /edæp/ and [meʃ] + /edæp/, while in an exclusively non-alternating block the phrases in sequence would be /lu/ + /edæp/ and /kɑn/ + /edæp/. Limited-context word2s only appear with one word1 type in the training trials; therefore, the other potential phrase is held-out from appearing in training. For instance, when /kisɑ/ appears in a phrase with an alternating word1 as in [me] + /kisɑ/, that would render [di] + /kisɑ/ a held-out phrase. The held-out phrases are incorporated in some of the testing trials. 55 Table 3-4. Pseudo-randomization structure inside each training block Training blocks word2 type “alternating word1” “non-alternating word1” n total 72=24×3 full-context full-context limited-context full-context full-context full-context full-context limited-context [dit] + /edæp/ [meʃ] + /edæp/ [me] + /kisɑ/ [dit] + /ufe/ [meʃ] + /ufe/ [di] + /peku/ [me] + /peku/ [di] + /budol/ /lu/ + /edæp/ /kɑn/ + /edæp/ /kɑn/ + /kisɑ/ /lu/ + /ufe/ /kɑn/ + /ufe/ /lu/ + /peku/ /kɑn/ + /peku/ /lu/ + /budol/ Upon the completion of the training trials, participants were informed that the testing phase could be initiated by clicking on the Next button on the page. In the following section, we will describe the specifics of the testing trials. 3.4.2. Testing In this section, participants engaged in two different types of 2-alternative forced-choice (2AFC) tasks, using key presses on a keyboard. The number of times the first choice or second choice was the correct answer was completely counterbalanced throughout each task. Throughout all trials, prompts were presented to participants simultaneously through both auditory and visual means, just as in the training phase. Before each task, participants had the opportunity to practice with two practice stimuli. Participants were advised to select the choice that initially appears correct to them with two warnings: first, they would not have the option to alter their answers, and second, after a prolonged pause (6 seconds), the trials would time-out automatically proceeding to the next item. The testing phase included 64 trials overall and the total duration of this phase was on average 15 (SD=5) minutes for all participants. The testing phase was organized into three blocks of testing trials. The first testing task was a phrase judgement task, and the second testing task was a segmentation task. In these first two tasks, both full-context and limited-context word2s were incorporated. Limited-context word2s here in the testing phrases refer to the word2s in the held-out word1 + word2 pairings not encountered by participants in training. The third testing task was a segmentation task incorporating only novel word2s. The following subsections provide further details regarding the stimuli and procedures for each task. For a comprehensive list of items in each task, please refer 56 to the Appendix A. Table 3-5 below outlines the chronological order of the testing tasks along with the template for the test items in each trial. Table 3-5. The structure of the tasks in the testing phase of the experiment Task Name Stimuli Type and Number Testing Task Template Practice n=2 Testing task 1 “Phrase Judgement” full phrase choices n=24+8 (familiar + held-out) [Word1+Word2] vs [Word1+Word2] Practice n=2 Testing task 2 “Familiar Segmentation” word2 choices n=12+4 (familiar + held-out) [Word1+Word2] + [Word2] vs [Word2] Testing task 3 “Novel Segmentation” word2 choices n=16 (novel) [Word1+Word2] + [Word2] vs [Word2] 3.4.2.1. Testing Task 1: Phrase Judgement The first forced choice task involved participants viewing an image while listening to two phrases featuring the combination of the same word1 and word2. The intended correct phrase either has appeared in the training or exactly matched the phonological patterns in the training items and the incorrect phrase was minimally different. Participants were instructed to choose the phrase that seems correct to them based on the alien language they have been exposed to in their training by pressing “Q” for the first and “P” for the second audio stimulus. All word1s and word2s presented were known by participants, as they had appeared during the training phase separately at least once. Although 8 out of 32 trials contained held-out phrases as they included limited-context word2s—only paired with one non-alternating and one alternating word1 in training. The stimuli were automatically concatenated using a Praat script, with a 75ms inter-stimulus interval (ISI) between the choices. The trials were labelled and categorized into 3 types based on their word1 type as well as the error type: “basic”, “alternating”, and “non-alternating”. Table 3-6 provides examples of choices coded as correct and incorrect for each trial type. The choices considered 57 incorrect contained specific errors with minimal differences so, unlike the correct choices, they did not match the patterns presented in the training trials. The 16 basic trials (B-A and B-NA) involved testing items constructed with both alternating and non-alternating word1s. The errors in the incorrect choices for the non-alternating word1s were specifically designed by either omitting the final consonant (/n/ of /kɑn/) before a vowel-initial word2 or by inserting an LC (after /lu/) before a consonant-initial word2. In contrast, the incorrect choices for the alternating word1s were created by swapping the LCs, that is changing /ʃ/ to /t/ and vice versa, and then by inserting the wrong LC either before a consonant-initial word2 or a vowel-initial word2 where an LC was already present. The 8 alternating trials (Alt) consisted of testing items made with the alternating word1s [meʃ/me] and [dit/di]. In this case, the errors in the incorrect choices were created by either omitting the LC before a vowel-initial word2 or inserting the LC before a consonant-initial word2. The 8 non-alternating trials (NonAlt) comprised testing items constructed with non-alternating word1s like /lu/ and /kɑn/ The errors in these incorrect choices arose from either removing the final consonant (/n/) before a consonant-initial word2 or inserting an LC between the vowel-final word1 and a vowel-initial word2. Table 3-6. Testing trial types in task 1 (phrase judgement) with examples Testing Trial Type Correct Incorrect Type of Error itemBasic (B-A) n=8 dikisɑ meʃæte diʃkisɑ meʃtæte inserting another LC with C-initial word2s inserting an extra LC with V-initial word2s itemBasic (B-NA) n=8 kɑnɑtæl lubudol kɑ_ɑtæl lutbudol deleting the final C of a non-alternating word1 inserting an LC at the end of a non-alternating word1 itemAltlternating (Alt) n=8 ditugæʃ mebudol di_ugæʃ meʃbudol deleting the LC inserting the LC itemNon-alternating (NonAlt) n=8 kɑnpeku luæte kɑ_peku luʃæte deleting final C of word1 inserting some LC after the word1 3.4.2.2. Testing Task 2: Familiar Segmentation In Task 2, the forced choice task was essentially a morpheme segmentation exercise. Participants viewed an image while listening to a phrase, which was followed by two choices representing potential realizations of the word2s from the phrase, as pronounced in isolation. Participants were 58 instructed to choose the isolated word referring to the object’s name that seems correct to them by pressing keys on the keyboard. Essentially, in this task participants decide on the segmentation of the words using their own intuitions because the training trials did not contain any isolated words. All the word2 choices were known by participants from the training phase, although 4 of the 16 trials included held-out phrases. The stimuli were concatenated automatically using a Praat script, with an inter-stimulus interval (ISI) of 100ms between the full phrase and the first choice, and a 75ms ISI between the two choices. In contrast to the previous task, task 2 only included alternating word1s, so the trials are categorized into just two types: "basic" and "alternating". Including non-alternating word1s /lu/ and /kɑn/ was deemed unsuitable for this task, as our primary interest lay in how participants address the ambiguity in parsing liaison consonants /ʃ/ and /t/. Table 3-7 illustrates examples of each item type. Basic trials (B-A) comprised testing items formed with word1s that did not have any liaison consonants (LC), meaning a consonant-initial word2 was present. In these trials, an incorrect choice resulted from misparsing the onset of word2 as an LC. Conversely, alternating trials (Alt) featured items constructed with words that included an LC, indicating that a vowel-initial word2 was used. Here, the incorrect choice stemmed from misparsing the LC as the word2’s onset. Table 3-7. Testing trial types in task 2 (familiar segmentation) with examples Testing Trial Type Prompt Correct Incorrect Type of Error itemBasic (B-A) n=8 mekisɑ dimæti kisɑ mæti isɑ æti misparse the onset of word2 as LC itemAltlternating (Alt) n=8 meʃido ditedæp ido edæp ʃido tedæp misparse the LC as the word2’s onset 3.4.2.3. Testing Task 3: Novel Segmentation In the last task, testing task 3, the forced choice task was essentially the same morpheme segmentation task as above but with a different stimulus type. Specifically, the word2s here were all novel word2s that did not appear in the training phase at all. In this task similar to the first task the trials were divided into 3 types based on their word1 type as well as the error type: “basic”, “alternating”, and “non-alternating”. Table 3-8 below shows examples of each trial type. The basic trials involved testing items that were constructed using word1s without any LC or final consonants, specifically when a consonant-initial word2 was present. In these trials, the incorrect response was due to misparsing the word2 as vowel-initial. 59 The alternating trials, on the other hand, included items with the LC, occurring when there was a vowel-initial word2. In these cases, the incorrect choice stemmed from misinterpreting the LC as belonging to word2. The non-alternating trials were solely comprised of /kɑn/, as it allowed for the inclusion of the final consonant to provide an incorrect option which could involve interpreting /n/ as belonging to the word2 (in contrast, /lu/ was used in the basic trials. Table 3-8. Testing trial types in task 3 (novel segmentation) with examples Testing Trial Type Prompt Correct Incorrect Type of Error itemBasic (B-A) n=4 mefærus ditʃægef færus tʃægef ærus ægef misparse the onset of the word2 as LC itemBasic (B-NA) n=4 lurunip runip unip misparse the onset of the word2 as LC itemAltlternating (Alt) n=4 ditɑjor meʃezɑ ɑjor ezɑ tɑjor ʃezɑ misparse the LC as the word2’s onset itemNon-alternating (NonAlt) n=4 kɑneʃin kɑnosu eʃin osu neʃin nosu misparse the final /n/ as the word2’s onset 3.5. Data collection procedure and data analysis The data collection procedures and methods for the experiment were according to the standards set by the UBC Behavioral Research Ethics Board and received their approval. Participants were recruited from the UBC linguistics participants pool in exchange for course credit for undergraduate-level linguistics courses. Potential participants were informed on the recruitment page that the study would involve learning sound patterns in an unfamiliar language and responding to some questions. All participants in this pool had to complete a language background questionnaire comprised of a comprehensive set of questions about all the languages they know or have experience with, as well as demographic information and relevant language disorders. To be eligible, participants must not have hearing loss. The language background eligibility criterion chosen was to only include participants that have not listed their L1(s) as French with an age of acquisition below four. This inclusion criterion was implemented to ensure participants shared a more homogeneous language background, thereby minimizing potential confounds arising from native-speaker intuitions regarding liaison-like patterns. 60 The experiment was executed using HTML and jsPsych, a JavaScript framework (de Leeuw, 2015), and was conducted remotely through a web browser. As a result, participants were able to take part in the experiment using their own desktop devices remotely. To ensure consistent audio quality and experimental conditions for all participants, a headphone check task (borrowed from Woods et al., 2017) was included. Participants were required to answer 4 of the 6 headphone check trials correctly to proceed to the experiment. After completing the experiment, the data was collected anonymously and securely stored on a UBC server in a comma-separated values (.csv) format. To prepare files for analysis, the researcher conducted pre-processing and data-cleaning procedures on the .csv files using specific packages in R Studio (version 2024.04.0). During this process, apart from the eligibility criteria, to ensure that the conclusions drawn from the data are robust and informative participant data were also removed based on predetermined performance exclusion criteria allowing the researcher to focus on the effects of the experimental manipulations. At first, the data of 4 participants were removed as they had mentioned the word “liaison” in their written feedback collected in the debriefing stage at the end of the experiment. Then the first of the predetermined exclusion criteria was applied to verify that participants were seriously engaged in the experiment. The participants who had over 10% of their total responses (n>7) classified as null answers—specifically, instances of not pressing a key during testing trials—were excluded. After this initial filtering, among the remaining participants, the next criterion was to ascertain that they understood the task and its objectives. To assess this, participants whose mean accuracy on basic items in each task fell more than two standard deviations below the overall mean of all participants were also excluded from the experiment. In total, the data from 43 participants were removed from the study. The Table 3-9 shows the summary of the excluded participants by condition. Table 3-9. Breakdown of participants exclusion by condition and criteria Finally, statistical analysis and modelling were performed using additional R packages, such as lme4 (Bates, et al., 2015). More details about the statistical models will be provided in the next chapter. Alternating 1st Non-alternating 1st Mixed total Recruited 82 83 76 241 Language Background 1 3 1 5 Debriefing 1 1 2 4 Null answers - 2 2 4 Basic items mean 9 11 10 30 After exclusion 71 66 61 198 61 Chapter 4 Results 4. Results In this chapter, the results of each testing task outlined in Chapter 3 are presented individually, beginning with a review of the descriptive statistics reflecting the raw accuracy rates of responses. The descriptive statistics of the empirical results displayed in the boxplots indicate the distribution of participants’ means. Following this, the outcomes of the inferential statistical analyses are reported. The data were analyzed using mixed-effects logistic regression models implemented in R through the lme4 package version 1.1-35.3 (Bates et al. 2015) and the emmeans package version 1.10.1 (Lenth et al. 2019), in addition to being plotted with the ggeffects package version 1.5.2 (Lüdecke, 2018). In all three tasks, the dependent variable is the participants' accuracy in the forced-choice tasks, treated as a binary variable coded as 0 (incorrect) and 1 (correct). The independent fixed variables in the analysis include training conditions in 3 levels (Alt1st=Alternating1st, NonAlt1st= Non-Alternating1st, Mix=Mixed), trial types in 4 levels (itemB-A=Basic-Alternating, itemB-NA=Basic-Non-Alternating, itemAltlt=Alternating, itemNonAltlt=Non-Alternating), and item familiarity in 2 levels (F=Familiar, H=Held-out). Additionally, all models incorporated random intercepts for both participants and items, random by-participant slopes for trial type and random by-item slopes for condition. To answer the research questions, mixed effects regression analysis was implemented to investigate statistically significant effects of the manipulated independent variables (training condition, trial type, and item familiarity or their interactions) on the accuracy of participants’ responses. 4.1. Task1 - Phrase Judgement The first 2AFC task included 32 trials with the full phrases (word1+word2) as choices. To observe differences between the learning trajectories as hypothesized, it is necessary to compare the overall performance of participants in the 3 training conditions in this task. Figure 4-1 below plots overall accuracy by condition. The means (and SDs) of the participant means in the three conditions are: Alt1st 0.79 (0.12), NAlt1st 0.76 (0.10), and Mix 0.81 (0.08). The notches on the boxplots indicate the 95% confidence interval of the median and the small point on the box indicates the mean. The box represents the interquartile range, encompassing the two middle quartiles on either side of the 62 median. By definition, this means that half of the participants fall within the box, while the other half lie outside of it. Notably, the overall mean accuracy as well as the 95% confidence interval ranges of the medians of the participants in all training conditions within this 32-trial task is above 0.69. This is a statistically above chance accuracy rate according to a right-tailed binomial test, with 0.05 alpha. Figure 4-1. Overall accuracy by condition in task 1 (phrase judgement) The trial types were categorized in 4 levels (total n 32 = 4 levels × 8 items): itemNonAlt, itemAltlt, itemB-A, itemB-NA. To better understand how the distribution of accuracy for participant responses in each training condition differ across the four trial types in this task and how trial types interact with conditions, it is important to compare the accuracy of participant responses to each trial type within the three conditions. As can be seen in the boxplots in Figure 4-2, for participants in all conditions, the itemB-A and itemB-NA (two boxes on the right) have similar distributions and their means are above 0.8 but their notch areas do not overlap with the itemAlt and itemNonAlt (two boxes on the left). The corresponding means (SDs) of each condition within the 4 trial types is also presented in Table 4-1 along with an example item (to see more examples, refer to Tables (3-6‒3-8) in Chapter 3). In the table, the highest mean value among the three conditions in each row (trial type) is underlined. 63 Table 4-1. Mean accuracy by condition across trial type in task 1 (phrase judgement) Trial Type Alt1st NAlt1st Mix itemNonAlt (n= 8) [luæte] vs [luʃæte] 0.71 (0.17) 0.64 (0.19) 0.75 (0.15) itemAlt (n= 8) [ditugæʃ] vs [diugæʃ] 0.78 (0.16) 0.76 (0.17) 0.77 (0.15) itemB-A (n= 8) [meʃæte] vs [meʃtæte] 0.82 (0.16) 0.83 (0.14) 0.85 (0.15) itemB-NA (n= 8) [lubudol] vs [lutbudol] 0.86 (0.16) 0.84 (0.16) 0.87 (013) Figure 4-2. Accuracy by condition across trial type in task 1 (phrase judgement) Figure 4-3 below shows the accuracy rates distributions of all participants in the three conditions to allow for a comparison of trials that contained familiar items (n=24) against held-out items (n=8). As can be seen in the boxplots, the distribution of the participant responses to familiar and held-out items overlap and their means are very close to each other for all conditions. 64 Figure 4-3. Accuracy by condition across item familiarity in task 1 (phrase judgement) A mixed-effects logistic regression model with the following formula shown in (1) including 4 fixed effects in addition to 2 random effects of intercept and slope for trial type by subject and intercept and slope for condition by item was fitted to the data. (1) responses ~ condition + trial_type + condition:trial_type + item_familiarity + (1 + trial_type | subject) + (1 + condition | item) The contrasts were treatment-coded where training condition (Alt1st=ref, NAlt1st, Mix), trial type (itemNonAlt=ref, itemB-A, itemB-NA, itemAltlt) and item familiarity (familiar=ref, held-out) and the interaction of condition and trial type were considered as fixed effects each with a reference level. The results showed two significant coefficient estimates: as for the training conditions, when the other variables are held constant at their respective reference levels, that is on itemNonA trials, and familiar items, participants in Alt1st were significantly more accurate than NAlt1st condition (β=-0.48, SE=0.21, p=0.02), and as for the item types, when other variables are held constant on Alt1st condition and familiar items, the responses to NonAlt trials was significantly less accurate than B-NA trials (β=1.2, SE=0.53, p=0.04). In the model comparisons with a chi-square likelihood ratio test, the model above (1) once compared to a simpler model without the fixed effect of condition (p= 0.02) and once without the fixed effect of trial type (p=0.007) was significantly different, but not significantly improved compared to a model without the item familiarity as a fixed effect. It is worth noting that comparing the model in (1) with a simpler model without interaction effects did not indicate significant improvement either. However, as it is important for the research question to know the between-condition differences, using the emmeans package theoretically relevant interaction differences were calculated. Table (4.2) shows all the comparisons based on the emmeans package calculated for all the interactions (estimated in differences in log odds), averaged over the item familiarity 65 variable with Bonferroni adjustment. As it is shown in the pairwise comparisons, the participants in Mix and the Alt1st conditions are more accurate than NAlt1st across all trial types; although the only statistically significant comparison is within their responses to the NonAlt items, where participants in NAlt1st were significantly less accurate than the Mix condition (β=-0.67, SE=0.21, p=0.00). The full model summaries can be found in the Appendix B1. Table 4-2. Pairwise comparisons in the statistical model based on the emmeans package in task 1 (phrase judgement) Contrast Trial type Estimate SE z.ratio p.value Alt1st - NonAlt1st itemNonAlt 0.48 0.21 2.31 0.06 itemAltlt 0.27 0.24 1.13 0.78 itemB_A 0.05 0.25 0.21 1.00 itemB_NA 0.28 0.28 0.99 0.96 Alt1st - Mix itemNonAlt -0.18 0.17 -1.10 0.82 itemAltlt 0.11 0.20 0.57 1.00 itemB_A -0.19 0.22 -0.85 1.00 itemB_NA -0.09 0.26 -0.34 1.00 NonAlt1st - Mix itemNonAlt -0.67 0.21 -3.20 0.00 itemAltlt -0.15 0.24 -0.66 1.00 itemB_A -0.24 0.26 -0.93 1.00 itemB_NA -0.37 0.29 -1.27 0.61 These comparisons can be viewed in Figure 4.4 which illustrates the predicted probability of accuracy from the mixed-effects logistic regression model. These probability values are averaged over the levels of item familiarity using marginal means. As can be seen from the lowest point (colored in light blue), the accuracy of participants in the NonAlt1st condition differ with other conditions on NonAlt trials more strongly with a bigger effect size. 66 Figure 4-4. Predicted probabilities of correct responses for each combination of condition and trial type in task 1 (phrase judgement) 4.2. Task 2 - Familiar Segmentation The second 2AFC task included 16 trials with the choices being between two potential word2s in the provided full phrase in the prompt. Similar to the previous task, to observe differences between the learning trajectories as hypothesized, it is necessary to compare the overall performance of participants in the 3 training conditions in this task. Figure 4.5 below plots overall accuracy by condition. The means (SD) of the participant means in the three conditions are almost at chance in this 16-trial task20: Alt1st 0.57 (0.15), NAlt1st 0.58 (0.16), and Mix 0.62 (0.17). 20 The term “at chance” here refers to a descriptive chance level of accuracy (8/16 trials). The binomial test was not used anymore to determine if this accuracy is significantly below or above chance level. 67 Figure 4-5. Overall accuracy by condition in task 2 (familiar segmentation) The trial types were categorized in 2 levels (total n 16= 2 levels × 8 items): itemAltlt, itemB-A. Figure 4-6 shows the accuracy of participants in the three conditions within different trial types to visualize how the distribution of participant responses in each training condition differ across the two trial types in this task and how trial type interacts with condition. The corresponding means (s.d.) are also presented in Table 4-3 along with example items. In the table, the highest mean value among conditions in each row (trial type) is underlined. The distribution of the two trial types is completely non-overlapping, however the participants in all conditions seem to perform similarly across trial types where all participant means within itemAlts are below 0.5 and all participant means within itemB-A are above 0.85. Table 4-3. Mean accuracy by condition across trial type in task 2 (familiar segmentation) Trial Type Alt1st NAlt1st Mix itemAlt (n= 8) [ditedæp] + [edæp] vs [tedæp] 0.38 (0.30) 0.41 (0.30) 0.50 (0.31) itemB-A (n= 8) [mekisɑ] + [kisɑ] vs [isɑ] 0.89 (0.15) 0.89 (0.17) 0.90 (0.13) 68 Figure 4-6. Accuracy by condition across trial type in task 2 (familiar segmentation) Figure 4-7 below shows the accuracy rate distributions of all participants in the three conditions to compare responses to trials that contained familiar items (n=12) against held-out items (n=4). As can be seen in the boxplots, similar to the previous task, the distribution of the responses to familiar and held-out items overlap in all conditions and their means are very close to each other. Figure 4-7. Accuracy by condition across item familiarity in task 2 (familiar segmentation) A mixed-effects logistic regression model with the following formula shown above in (1) including 4 fixed effects in addition to 2 random effects of intercept and slope for trial type by subject and intercept and slope for condition by item was fitted to the data. 69 The contrasts were treatment coded where training condition (Alt1st=ref, NAlt1st, Mix), trial type (itemAltlt=ref, itemB-A) and item familiarity (familiar=ref, held-out) and the interaction of condition and trial type was considered as fixed effects each with a reference level. The results showed only one significant coefficient estimate as the other variables are held constant on Alt1st and familiar items, the itemAltlt compared to the itemB-A were significantly worse (β=4.47, SE=0.41, p<0.001). The full model summaries can be found in the Appendix B2. In the model comparisons with a chi-square likelihood ratio test, the model above (1) compared to a simpler model without the fixed effect of trial type (p=0) was significantly different, but not significantly improved compare to a model without the item familiarity and condition as fixed effects separately. It is worth noting that comparing the following model with a simpler model without interaction effects with a chi-square likelihood ratio test did not indicate significant improvement either. Nevertheless, using the emmeans package theoretically relevant interaction differences were calculated. As it is shown in the pairwise comparisons in Table 4-4, across all trial types the participants in NAlt1st and the Alt1st conditions are less accurate than Mix while participants in Alt1st are less accurate than NAlt1st. Although, none of the pairwise comparisons are statistically significant. Table 4-4. Pairwise comparisons in the statistical model based on the emmeans package in task 2 (familiar segmentation) Contrast Trial type Estimate SE z.ratio p.value Alt1st - NonAlt1st itemAltlt -0.21 0.44 -0.47 1.00 itemB_A -0.61 0.50 -1.22 0.67 NonAlt1st - Mix item_A -0.40 0.46 -0.87 1.00 itemB_A -0.10 0.34 -0.31 1.00 Alt1st - Mix itemAltlt -0.44 0.43 -1.03 0.90 itemB_A -0.34 0.37 -0.89 1.00 These comparisons can be viewed in Figure 4-8 which illustrates the predicted probability of a correct response from the mixed-effects logistic regression model. These probability values are averaged over the levels of item familiarity using marginal means. As can be seen from the lower point (colored in blue), the performance of participants on the itemAltlt trials is close to floor while their performance on itemB-A trials is close to the ceiling. 70 Figure 4-8. Predicted probabilities of correct responses for each combination of condition and trial type in task 2 (familiar segmentation) 4.3. Task 3 - Novel Segmentation The third 2AFC task was similar to the previous task except all the word2s were novel; therefore, the item familiarity variable is irrelevant here. To observe differences between the learning trajectories as hypothesized, the training conditions’ overall performances are compared in Figure 4-9 below. The means (SDs) of the participant means in the three conditions are almost at chance21: Alt1st 0.57 (0.14), NAlt1st 0.58 (0.16), and Mix 0.64 (0.17). 21 The term “at chance” here refers to a descriptive chance level of accuracy (8/16 trials). The binomial test was not used anymore to determine if this accuracy is significantly below or above chance level. 71 Figure 4-9. Overall accuracy by condition in task 3 (novel segmentation) The trial types were categorized in 4 levels (total n 16 = 4 levels × 4 items): itemNonAlt, itemAltlt, itemB-A, itemB-NA. Figure 4-10 shows the accuracy of conditions within different trial types, to better understand how the distribution of participant responses in the three training conditions differs across different trial types in this task and how trial types interact with conditions. As can be seen in the boxplots, for all participants, the B items (two boxes on the right) have similar distributions and their means are above 0.8 whereas within the A and NonA items (two boxes on the left) there is more variability. The corresponding means (SD) are also presented in Table 4-5 along with an example item. In the table, the highest mean value among conditions in each row (trial type) is underlined. 72 Table 4-5. Mean accuracy by condition across trial type in task 3 (novel segmentation) Trial Type Alt1st NAlt1st Mix itemNonAlt (n= 4) [kɑneʃin] + [eʃin] vs [neʃin] 0.54 (0.29) 0.63 (0.29) 0.68 (0.32) itemAlt (n= 4) [ditɑjor] + [ɑjor] vs [tɑjor] 0.55 (0.32) 0.53 (0.28) 0.63 (0.33) itemB-A (n= 4) [mefærus] + [færus] vs [ærus] 0.86 (0.24) 0.89 (0.19) 0.90 (0.19) itemB-NA (n= 4) [lurunip] + [runip] vs [unip] 0.88 (0.18) 0.79 (0.23) 0.89 (0.18) Figure 4-10. Accuracy by condition across trial type in task 3 (novel segmentation) A mixed-effects logistic regression model with the following formula (2) including 3 fixed effects of condition, trial_type, and the interaction of condition and trial_type in addition to 2 random effects of intercept and slope by subject and intercept and slope by item was fitted to the data: (2) responses ~ condition + trial_type + condition:rial_type + (1 + trial_type | subject) + (1 + condition | item) The contrasts were treatment coded where training condition (Alt1st=ref, NAlt1st, Mix), item type (itemNonAlt=ref, itemB-A, itemB-NA, itemAlt) and the interaction of condition and item type were considered as fixed effects each with a reference level. The results showed multiple significant coefficient estimates: when the other variables are held constant at their respective reference levels, that is on itemNonA trials, and familiar items, among the training conditions, participants in Alt1st were significantly less accurate than Mix (β=0.99, SE=0.49, p=0.05), and 73 when the other variables are held constant at their respective reference levels, that is on Alt1st condition, and familiar items, among the item types, all differences were significant: participant responses to NonA were less than B-NA items (β=3.51, SE=0.44, p=0), responses to NonA was less than B-A items (β=4.04, SE=0.51, p=0), and responses to NonA was higher than A items (β=-1.72, SE=0.34, p=0). The full model summaries can be found in the Appendix B3. In the model comparisons with a chi-square likelihood ratio test, the model above (2) once compared to a simpler model without the fixed effect of condition (p= 0.02) and once without the fixed effect of trial type (p=0) was significantly different. It is noteworthy that comparing the following model with a simpler model without interaction effects with a chi-square likelihood ratio test did not indicate significant improvement. Regardless, using the emmeans package theoretically relevant interaction differences were calculated. As it is shown in the pairwise comparisons in Table 4-6, across the itemNonAlt, itemAlt, itemB-A trial types the participants in the Alt1st conditions are less accurate than NonAlt1st and Mix. Although, none of the pairwise comparisons are statistically significant. Table 4-6. Pairwise comparisons in the statistical model based on the emmeans package in task 3 (novel segmentation) Contrast Trial type Estimate SE z.ratio p.value Alt1st - NonAlt1st itemNonAlt -0.46 0.50 -0.92 1.00 itemAlt -0.42 0.63 -0.66 1.00 itemB_A -0.27 0.50 -0.53 1.00 itemB_NA 0.73 0.35 2.11 0.10 Alt1st - Mix itemNonAlt -0.99 0.49 -1.99 0.14 itemAlt -1.46 0.62 -2.35 0.06 itemB_A -0.16 0.49 -0.31 1.00 itemB_NA 0.06 0.35 0.16 1.00 NonAlt1st - Mix itemNonAlt -0.53 0.50 -1.05 0.88 itemAlt -1.05 0.62 -1.68 0.28 itemB_A 0.11 0.50 0.22 1.00 itemB_NA -0.68 0.33 -2.05 0.12 74 These comparisons can be viewed in Figure 4-11 which illustrates the predicted probability of accuracy on the task, based on population-level predictions from the mixed-effects logistic regression model. Figure 4-11. Predicted probabilities of correct responses for each combination of condition and trial type in task 3 (novel segmentation) 4.4. Task 2 and 3 – Both Segmentation Tasks In sections 4.2 and 4.3 the two segmentation tasks were analyzed separately. To analyze both tasks together, the trial types are categorized based on the word2s. In order to test if different word2 types have a statistically significant effect on participants’ performance, the trials are categorized in terms of whether the intended word2 in the phrase was C-initial or V-initial. This is equivalent to merging the itemAlt and itemNonAlt levels under the V-initial trials and merging itemB-A and itemB-NA levels together under the C-initial trials. Item familiarity has 3 levels here, familiar (phrases that occurred in training), held-out (phrases that did not occur training but the word1s and word2s appeared in training individually), and novel (phrases that did not occur in training because the word2s were absent in training), unlike the previous models. A mixed-effects logistic regression model with the following formula (3) including fixed effects of condition, trial type (based on word2), item familiarity, and the interaction of condition and trial type in addition to 2 random effects of intercept and slope by subject and intercept and slope by item was fitted to the data: 75 (3) responses ~ condition + trial_type + condition:trial_type + item_familiarity + (1 + trial_type | subject) + (1 + condition | item) The contrasts were treatment-coded where training condition (Alt1st=ref, NAlt1st, Mix), trial types were divided into 2 levels based on their word2 shape (C-initial=ref, V-initial) and item familiarity in 3 levels (familiar=ref, held-out, novel) and the interaction of condition and trial type as fixed effects each with a reference level. The results showed only one significant coefficient estimatewhen the other variables are held constant on Alt1st condition, and familiar items, the C-initial word2s were more accurate than V-initial word2s (β=-4.24, SE=0.40, p=0). Figure 4-12 illustrates the predicted probability of accuracy on both segmentation tasks responses combined. These probability values are averaged over the levels of item familiarity using marginal means. Figure 4-12. Predicted probabilities of correct responses for each combination of condition and trial type in task 2 and 3 (segmentations) In the model comparisons with a chi-square likelihood ratio test, a model with 3 fixed effects once compared to a simpler model without the fixed effect of trial type (p=0) was significantly different and once without the fixed effect of condition was nearly significant (p=0.05), but not significantly different without the item familiarity. The model above (3) was not significantly improved compared to a model without interaction effect. The full model summaries can be found in the Appendix B4. 76 Chapter 5 Discussion 5. Discussion In this chapter, the results presented in Chapter 4 will be discussed as they relate to the hypotheses and predictions stated in Chapter 2 Section 2.5. The main research question will be discussed in Section 5.1 in light of the main findings about the effect of the order of input data or test trial type on learning followed by the discussion of the predictions regarding the three dimensions of learning in Section 5.2. Subsequently, Section 5.3 discusses the effect of universal biases in segmentation, and Section 5.4 discusses the analysis of the successful learners. Finally, Section 5.5 includes the conclusion and presents future research. 5.1. The effect of all the independent variables on learning By designing an artificial mini-language exhibiting morpheme-specific phonological patterns, the aim in this implicit learning experiment was to induce inconsistencies in the phonological system underlying the input data. The motivation behind the primary research question was to investigate in what ways the structure of the input data, specifically the arrangement of blocks of training data affects learning. Based on a theory of learning with an error-driven learning algorithm, assuming the same initial state, and the same final state of learning theoretically for all learners in the three conditions of the experiment, the rationale was that structured input data would influence the learning trajectory of learners. The null hypotheses were that learning for all participants in the different conditions would be equally difficult; additionally, that the difficulty of learning would not depend on test trial types. In contrast to these null hypotheses, I would expect that except for item familiarity, the other independent variables in the experiment—training condition (i.e., the learning trajectory), test trial type and their interaction—would be significant predictors of participants’ performance in testing. According to our predictions provided in Section 2.5 in Chapter 2, if the learning trajectories in each condition affect the three aspects in learning and participants’ responses, participants’ performance in each condition would reflect the difficulty in the expected direction. Additionally, if the learning trajectories in each condition affect the extent to which learners learn various items, participants’ performance in each condition would depend on the test trial type. 77 The results presented in the previous chapter, analyzed through statistical models and post-hoc chi-square likelihood ratio tests indicate the following conclusions regarding our null hypotheses. The interaction of training conditions and test trial types did not significantly improve the model fit, therefore failing to reject our null hypothesis that differences in performance between participants in the three conditions does not depend on the test trial type. With respect to the other fixed effects in the statistical analysis, the inclusion of the three training conditions, each with a different learning input data structure, significantly improved the model fit. Therefore, this result rejects the null hypothesis that training condition has no effect on participant responses; albeit with the caveat that these results support the prediction only in 2 out of the 3 tasks: task 1 (the phrase judgement task), and task 3 (the novel segmentation task), and not task2 (the familiar segmentation task). The inclusion of test trial types, each with a different item and error type, improved the model fit in all tasks, therefore rejecting the null hypothesis that test trial type has no effect on participant responses. It is important to note that the fixed effect of item familiarity, the distinction between familiar and held-out phrases, was not a significant predictor in any of the tasks, which fails to reject the null hypothesis that item familiarity has no effect on participant responses. I predicted that item familiarity would be the only independent variable not involved in affecting participant response. Thus, in this case, failure to reject the null hypothesis supports the initial prediction about item familiarity. This result could be interpreted as an indication that the performance of participants did not rely on memorization of the items in the phrase judgement task and the segmentation task. Although from a different perspective, it is worth mentioning that having combined the two segmentation tasks in one model as presented in Section 4.4, item familiarity with three levels (familiar, held-out, novel) did not significantly improve the model fit. In other words, participants’ overall performance in the segmentation tasks is not predicted by item familiarity. In the next section, I will discuss the accuracy of participants in each condition on various types of testing trials in the same task as well as across tasks to assess the specific predictions about the three aspects of learning. 5.2. The effect of the interaction of input data structure and test trial types on learning In an error-driven learning theory, as learning progresses during the training phase, participants engage in strategies involved in the components of learning and employ mechanisms to construct the constraint hierarchy and the final state grammar. These components of learning which are generally thought to occur iteratively and in parallel, involve interpreting the structure of the output 78 (phonological and morphological structure) and computing the underlying representation (Tesar and Smolensky, 2000). By the time the learners finish the training phase they must also employ a mechanism to resolve the inconsistency caused by the alternating and non-alternating morphemes. The experimental design for the testing phase operates under the set of assumptions that all participants by the end of the training have established a UR for each morpheme and a constraint hierarchy as their end-state grammar. In each forced-choice trial, their choice corresponds to the optimal candidate that emerges from the final-state grammar given the underlying representation they have posited for each particular morpheme. The responses coded as correct in the forced choice tasks are based on the optimal outputs from the end state grammar and the particular set of underlying representations predicted within the learnability framework outlined in Section 2.5. In order to effectively analyze the dimensions of learning, the testing trials were categorized by the types of errors and the specific word1 types. The participants in the three conditions experience distinct learning trajectories as receiving the input learning data in different orders is expected to influence the extent to which these dimensions are hard to learn. Based on this rationale, I hypothesized that there would be differential learning between participants in the three conditions, qualitatively and quantitatively. Specifically, I predicted that different learning trajectories could lead to differences in the accuracy rates among participants in the three conditions. In my hypothesis, the quantitative difference refers to the extent to which the participants have been affected in 1 (or more) dimension of their learning: underlying representation of the alternating morphemes reranking stages, and constraint cloning or lexicon indexation. The qualitative difference refers to differences in participants’ performance on trial types within each condition. As mentioned in the previous section, the prediction about the qualitative difference was not supported; that is, the null hypothesis regarding the interaction of condition and trial type was not rejected. As for the quantitative difference, the null hypothesis was rejected in the phrase judgement task and the novel segmentation task. Although, regardless of significant differences between conditions within some trial types in the pairwise comparisons, none of the predicted differences between conditions were observed. To discuss the current findings and their significance, all the relevant tasks and the items are discussed under each prediction separately in the following subsections. 5.2.1. Computing the underlying representation (in alternations) The first prediction was about the dimension of learning where differences in learning data and trajectory are expected to affect the learning of underlying representations in alternations. The interdependent and iterative nature of the strategies to compute underlying representations and to 79 construct hierarchies given an output in different components of learning makes it challenging to isolate their effect in the learning outcome. Nevertheless, if the effect of the learning trajectory is strong enough, we could observe differences in performance. The prediction was that the learning trajectory of the participants in the Alt1st condition would be more advantageous for acquiring the underlying representations of the alternating morphemes (itemAlts and itemB-As in testing) because their input data is superior to that of other conditions. The initial data that the Alt1st condition participants receive in their first block makes them aware of the alternation sooner in their trajectory than others since they get the contrastive paradigm of different liaison consonants before the same word2 as shown in Section 3.4.1, copied below in Table 5-1. For instance, when a V-initial word2 such as /ibud/ ‘camera’ appears in a phrase, the pseudo-randomization ensures that the same word2 appears in the next phrase. In this way, both alternating word1s appear consecutively in the same word2 context: /ditibud/, /meʃibud/, … which is expected to facilitate the learners’ understanding of segmentation, and eventually the underlying representation. In terms of proportions, in each block, in the Alt1st and NonAlt1st conditions, 12 out of the 24 unique phrases contain V-initial word2s. With the specific arrangement of pseudo-randomization shown in Table 5-1, 8 phrases out of the 12 phrases with V-initial word2s always appear in pairs. This distribution was intended to reduce the probability of the word2s being coincidentally re-analyzed as /ʃ/- or /t/-initial words. The participants in the NonAlt1st condition do not experience this paradigm in their first block of training, so they are expected to be at a disadvantage. The Mix condition only gets one alternating word1 in each of their blocks so according to this argument their accuracy rate would be between the Alt1st and the NonAlt1st condition. Table 5-1. Pseudo-randomization order for Alt1st condition Block 1 “alternating word1s” → Block 2 “non-alternating word1s” /dit/ + /ibud/ /meʃ/ + /ibud/ /me/ + /kisɑ/ /dit/ + /ufe/ /meʃ/ + /ufe/ /di/ + /peku/ /me/ + /peku/ /di/ + /budol/ … /lu/ + /ibud/ /kɑn/ + /ibud/ /kɑn/ + /kisɑ/ /lu/ + /ufe/ /kɑn/ + /ufe/ /lu/ + /peku/ /kɑn/ + /peku/ /lu/ + /budol/ … 80 Contrary to our predictions, the statistical analysis of the two segmentation tasks did not find any significant differences in the interaction of trial types and conditions. However, the results of the pairwise comparisons from the novel segmentation task show that within the itemAlt trials (alternating word1s) when the item familiarity is held constant the participants in the Mix are more accurate than Alt1st. This comparison was not technically statistically significant but it is being reported as the p-value was approaching significance (p= 0.06). Table 5-2. Predictions and results of learning the underlying representation Prediction Results Task – Item type Alt1st > Mix > NonAlt1st ❌ Mix > Alt1s (nearly significant) Novel Segmentation itemAlt To understand this result in the context of our predictions, it is important to examine how the three conditions performed throughout the segmentation trials. The goal behind these two tasks was to test participants’ knowledge of the word boundaries which could in turn reveal to what extent they have learned the allomorphy, and if not what the reasons could be. Table 5-3 shows the possible combinations of trial types schematically in terms of response accuracy. The “correct/incorrect” status indicates highly accurate/inaccurate responses and “uncertain” indicates near-chance level accuracy of responses. 81 Table 5-3. Schema of possible interpretations based on trial types in segmentation tasks C-initial word2 (itemB-A, itemB-NA) V-initial word2 (itemAlt, itemNonAlt) Interpretation a. correct correct learned the allomorphy → possibly also the maximal CVC form as the UR b. correct incorrect the word1 is always CV → did not learn the allomorphy, blocked by a segmentation bias c. correct uncertain the word1 is CV more often than not → learning of the allomorphy is hindered by a segmentation bias d. uncertain correct the word1 is CVC more often than not → did not fully learn the allomorphy e. incorrect correct learned some kind of alternation but not the intended allomorphy (where the word1 is CVC with an alternating coda but not just /t/ and /ʃ/) The predicted probability values from the analysis of the segmentation tasks in Section 4.2 and 4.3 are summarized in Table 5-4 below. These accuracy probabilities indicate that both the participants in the Alt1st condition and the Mix have chosen the correct choice (>0.89) on the C-initial word2s in the two segmentation tasks, however the V-initial word2 trials are where they slightly differ. In the familiar segmentation task, within V-initial word2s (the itemAlts) all the participants, regardless of condition, have low accuracies (< 0.23), although the participants in Alt1st are slightly more inclined to choose the CV form than the rest. When participants’ knowledge is probed with novel word2s in the novel segmentation task, within the V-initial word2s (here both the itemAlt and itemNonAlts) the probabilities indicate that the performance of the participants in the Mix condition are slightly higher (0.32) compared to others. It was in this task where within itemAlts, the comparison of performance of the participants in the two conditions Alt1st and Mix was approaching a statistically significant difference. It is also interesting that participants in the Alt1st condition have the same low probability of accuracy in the two segmentation tasks. 82 Table 5-4. Predicted probabilities (95% CI) in V-initial and C-initial trials in segmentation tasks Alt1st NonAlt1st Mix C-initial – familiar segmentation 0.93 (±0.01) 0.94 (±0.01) 0.95 (±0.01) C-initial – novel segmentation 0.93 (±0.01) 0.89 (±0.02) 0.93 (±0.02) V-initial – familiar segmentation 0.14 (±0.03) 0.17 (±0.04) 0.23 (±0.07) V-initial – novel segmentation 0.14 (±0.04) 0.2 (±0.05) 0.32 (±0.08) The predicted probabilities inboth tasks taken together across various item types underscores the challenges associated with parsing the liaison consonant in ambiguous scenarios. As it has been discussed in the context of child errors and developmental trajectory in Section 2.3, this challenge arises in early stages of learning when universal constraints in favour of left-edge alignment of phonological and morphological structure lead to certain biases during word segmentation favouring more C-initial parsing of word2s instead of V-initial. This matches the interpretation (c) and to some extent (b) in Table 5-3 where the word1 more often than not is in the CV form. In this context, a more nuanced interpretation of the results suggests that the Mix condition has not necessarily mastered the allomorphy more effectively than the Alt1st condition since their predicted probability of a correct response is below 0.5. Rather, the participants in the Mix condition appear to have been able to overcome the segmentation bias to some extent comparatively. This topic is discussed in more detail in this chapter in Section 5.5. To discuss this issue from the perspective of the predictions of the learnability theory, it is useful to review the role of the universal markedness constraints in the forced-choice tasks. Align-L is the markedness constraint which directly influences segmentation through alignment requirements in parallel to other components of learning. A successful learner must learn the correct ranking of this constraint in relation to other constraints in the constraint hierarchy to learn the allomorphy pattern and infer the correct underlying representation. In the testing trials labelled itemAlt, the phrases were made from alternating word1 + V-initial word2. As can be seen from the tableau below in (1) with the example stimuli [ditogi] and choices /togi/ vs /ogi/, the intended correct choice in the segmentation task is the candidate that violates Align-L, given that the underlying representation is /dit/ + /ogi/ as assumed in the analysis in Section 2.4.2. 83 (1) ALIGN-L ☞ a. [di.to.gi]  /di.t#o.gi/ * b. [di.to.gi]  /di.#to.gi/ Whereas, in the trials labelled B-A the phrases were made from alternating word1 + C-initial word2. As can be seen from the tableau below in (2) with the example stimuli [mekisɑ] and choices /kisɑ/ vs /isɑ/, the intended correct choice in the segmentation task does not violate Align-L, given that the underlying representation is /me/ + /kisɑ/ as assumed in the analysis. (2) ALIGN-L ☞ a. [me.ki.sɑ]  /me.#ki.sɑ/ b. [me.ki.sɑ]  /me.k#isɑ/ * In the assumed biased initial state in the grammar, the Align-L constraint along with other markedness constraints outrank faithfulness constraints. Learning to demote Align-L must occur during block 1 for all learners due to errors with phrases containing /meʃ/ and /dit/ (e.g. [me.ʃ#o.gi]) as well as /kɑn/ (e.g. [ka.n#o.gi]) or both depending on the condition. It is crucial that these errors would occur only if the underlying representations for the word1s posited by the learners were the CVC forms. Thus, by the time all the participants in the three conditions reach the end of the first block of training, Align-L is expected to have been demoted in their constraint hierarchies at that stage. These two strategies, that is constraint demotion and learning the correct segmentation and ultimately considering the CVC form to be the underlying form are part of the iterative loop in the learning algorithm that eventually enables participants to master the alternation pattern in their learning data. However, as the results of the segmentation tasks have shown, the majority of participants, regardless of condition, chose candidate (b) in tableau (1) while they picked candidate (a) in tableau (2); therefore, they preferred parsing the word2s as C-initial. The results of the phrase judgement task reported in Section 4.1 show that the three conditions are highly accurate in forced choice tasks of a different type with alternating items. In this task, in an itemAlt trial, to use the same phrases as an example, when choosing between /ditogi/ vs /diogi/ or /mekisɑ/ vs /meʃkisɑ/, majority of the participants choose the intended correct choice of /ditogi/ and /mekisɑ/. This choice could have also stemmed from a C-initial underlying representation for the word2 (/togi/ or /kisɑ/). Therefore, with the lack of significant differential learning outcomes, it is not simple to pinpoint which part of the aforementioned loop was difficult for the participants and where they deviated 84 from it compared to the hypothesized algorithm for an ideal learner. However, as these two tableaux indicate, Align-L is the constraint which all participants prefer to satisfy. The answer as to why the difference between the Mix and Alt1st, though only approaching significance, is in the opposite direction to our predictions requires further research. If the interpretation that the Mix condition is able to overcome (or is less impacted) by the segmentation bias is on the right track, one potential explanation could be that a more varied context of word1s preceding the same word2 might better accentuate the boundary between word1 and word2. That could lead to the use of the heuristic I proposed in Section 2.4 about choosing the maximal form as the underlying representation. For instance, as illustrated in below in Table 5-5, V-initial word2s like /ibud/ appear in both alternating and non-alternating word1 contexts across both blocks sequentially. Table 5-5. Pseudo-randomization order in the Mixed condition Block1 “(non/)alternating word1” → Block2 “(non/)alternating word1s” /kɑn/ + /ibud/ /meʃ/ + /ibud/ /me/ + /kisɑ/ /kɑn/ + /ufe/ /meʃ/ + /ufe/ /kɑn/ + /peku/ /me/ + /peku/ /kɑn/ + /budol/ … /lu/ + /ibud/ /dit/ + /ibud/ /di/ + /kisɑ/ /lu/ + /ufe/ /dit/ + /ufe/ /lu/ + /peku/ /dit/ + /peku/ /lu/ + /budol/ … Another possible explanation may relate to the context in which the constraint demotion algorithm operates in learning. Given the correct underlying representation posited for the ideal learners, the only error arising from the Alt1st condition training data in their first block stems from the wrong ranking of Align-L and Max. As shown in example (27b) in Section 2.5.1, initially the learner makes errors with considering an incorrect output such as [me.#i.bud] due to a ranking of NOV.V, NOC.C, ALIGN-L >> MAX in their initial-state constraint hierarchy. None of the other markedness constraints require demotion besides ALIGN-L, as they are not the loser preferring constraints with the alternating morphemes. It is important to remember that this specific error relies on the underlying representations posited; if the underlying representation is not /dit/ or 85 /meʃ/, the loser preferring constraints would be different. However assuming that the underlying representation is in place as we assumed, given that ALIGN-L is considered a markedness constraint and the syllable structure in general in the first block is in line with the universal markedness bias in the initial-state, learning a language-specific (non-universal) pattern starting with errors that violate only one markedness constraint might have been more difficult for the participants in the Alt1st condition. In other words, breaking the feedback loop of the initial state and realizing that violating universal markedness constraints is in fact necessary in this language might have been more challenging for participants in the Alt1st condition. Whereas for learners of the other conditions, there is more than one markedness constraint that is loser preferring from the start in the first block. 5.2.2. Reranking stages The second prediction was about the error-driven reranking stages of the grammar. Based on the learnability theory of an ideal learner, the prediction was that for the NonAlt1st condition it would be easier to learn the final-state constraint hierarchy because they have the shortest trajectory to get to the final-state. However, contrary to our predictions, the participants in the NonAlt1st condition are lower in accuracy compared to Mix within the itemNonAlts when the other variables are held constant in the pairwise comparisons. Also, even though not statistically significant, the participants in the Alt1st condition are higher in accuracy compared to NonAlt1st within itemNonAlt (p=0.06). Table 5-6. Predictions and results of reranking stages Prediction Results Task – Item type NonAlt1st > Alt1st > Mix ❌ Mix > NonAlt1st Alt1st > NonAlt1st* (*nearly significant) Judgement – itemNonAlt Judgement – itemNonAlt To explore how this significant difference came about and what it could imply about the differences and similarities in the learning trajectories, I will compare the results for each item type. 86 Significant difference between NonAlt1st and Mix within itemNonAs The first subtype of the itemNonAlts (n=4 familiar) is the choices made with the CVC word1 /kɑn/ and C-initial word2 as can be seen from the tableau below (3) with the example stimuli [kɑndʒomet] vs [kɑdʒomet]. The four items were familiar combinations exactly matching the training stimuli. (3) /kɑn # dʒomet/ NoC.C-L Max NoC.C ☞ a. [kɑn.dʒomet] * b. [kɑ.dʒomet] * By choosing the suboptimal candidate [kɑdʒomet] participants would be making an error, which could be due to three possibilities: a. The learners know the correct underlying representation but they have not learned the correct ranking but instead have a ranking where MAX is outranked by NOC.C; b. The learners have learned the correct ranking as above where NOC.C-L is at the top but failed to correctly limit the indexed lexicon, so they have expanded it and considered /kɑn/ to also be part of the -L indexed lexicon; c. They have not learned the correct underlying representation for /kɑn/ and think the underlying representation is actually /kɑ/. The second subtype of the itemNonAs (n=2 familiar+2 heldout) is the choice made with the CV word1 /lu/ and the liaison consonant /ʃ/ + V-initial word2 as can be seen from the tableau below with the example stimuli [luæte] vs [luʃæte]. Two of these items were familiar combinations and two items were unfamiliar22. (4) /lu # æte/ MAX DEP NOV.V ALIGN-L ☞ a. [lu.æte] * b. [lu.ʃæte] * * The errors in these subitems could be due to two possible reasons: a. The learners have learned the correct underlying representation but have not learned the correct ranking but instead have a ranking where NOV.V outranks the faithfulness constraint DEP; 22 Note that, due to the limitations in the design, both of the held-out phrases in the itemNonAs were with /lu/+word2 combinations. 87 b. The second reason could be due to a wrong underlying representation. However, it is far-fetched to assume that participants stored the underlying representation of the word1 as /luʃ/ mistakenly, as that combination never occurs. It is more probable that the word2s start with /ʃ/ since the word2s might appear after these liaison consonants in training. Comparing the descriptive statistics for these two subtypes would allow a more detailed interpretation of how these two conditions might be different. Table 5-7 shows the mean accuracy of three conditions within itemNonAlts. These means show that NonAlt1st is less accurate than the Mix condition in both of the non-alternating word1s. Table 5-7. Average accuracy in the two subtypes of itemNonAlt trials in task 1 (phrase judgement) Alt1st NonAlt1st Mix /kɑn/ + C-initial 0.84 0.74 0.87 /lu/ + V-initial 0.57 0.54 0.63 Why would the NonAlt1st condition be worse with the word1s that they learned in their first block? One possible explanation for the overall lower accuracy of NonAlt1st is a recency effect in memory. If the interpretation that the NonAlt1st condition does not have the correct ranking that allows them to pick the optimal candidate is correct; then for them, NOV.V, NOC.C >> MAX, DEP seems to be the decisive ranking. This may be due to the fact that the recent syllable structure in the output that the participants in the NonAlt1st condition was exposed to just before this testing task consists of patterns of phonologically motivated alternations with unmarked structures. Interpreting the constraint hierarchy in the structure of the more recent alternating training trials could have influenced the choices of participants. On the other hand, if the recency effect was a strong bias in general in the experiment, we would expect to observe the Alt1st condition to be less accurate within itemAlts. However, that is not the case; no significant differences were found within itemAlts. Therefore, if there is in fact a memory effect, as suggested by the statistical analysis, it seems to be affecting the learning of the NonAlt1st condition more strongly. Furthermore, the means in Table 5-7 above show that in trials involving /lu/, all conditions are on average relatively uncertain in their responses (mean=0.5‒0.65), and it is not just the participants in the NonAlt1st condition that have been affected by their recent experience. The participants in the other two conditions (Alt1st and Mix) are highly accurate in /kɑn/ items but their accuracy drops to near chance levels with /lu/ items. This consistent uncertainty can be attributed to a combination of two possible reasons: 88 a. The segmentation results indicate learning the correct representation of the V-initial word2s was challenging for all participants. Therefore, this result could have been caused by some of the participants being open to a segmentation of the phrases as /lu/ + /ʃ/-initial word2s; b. The tendency to resist the violation of the NOV.V constraint could be shared by all conditions. Near significant difference between Alt1st and NonAlt1st within itemNonAlts Similar to the Mix vs NonAlt1st differences reviewed before, the predicted probabilities of the correct responses in the three conditions across different item types, as reported in Section 4.1, indicate that the only item type wherein the Alt1st and the NonAlt1st condition seem to perform differently from each other is within the itemNonAlts. The better performance of Alt1st compared to the NonAlt1st condition within itemNonAlts in this task is also against the predictions with respect to the reranking stages. The results of the segmentation tasks did not confirm the prediction regarding the successful learning of the underlying representation by the Alt1st condition; therefore, this could not have acted as a leverage for them. In fact, the Alt1st and the Mix condition accuracy is similar and above chance level across different item types in this task. 5.2.3. Constraint cloning and lexicon indexation Our predictions suggested that the non-uniform data of the Mix condition in both blocks of training should place them at a disadvantage compared to the ordered conditions. They have to cope with inconsistencies with their input data consisting of only one alternating word1 at a time. There were no predictions about the specific advantages between the two ordered conditions based on the learnability theory of an ideal learner reviewed in Section 2.5.1 and 2.5.2. Although, from the perspective of a suboptimal learner that might be affected by memory limitations, the trajectory for the participants in the Alt1st condition could have put them at a disadvantage because resolving the inconsistency theoretically relies on participants recalling the combination of word1s+word2s learned in the first block to be tested against their updated grammar in the second block without encountering them again. In other words, learners in the two ordered conditions are expected to resolve the inconsistency in the second block. For the NonAlt1st condition the errors stored in the archive in the second block would also lead to the inconsistency and then resolving the inconsistency in the same block. Whereas for the Alt1st condition, detecting the inconsistency relies on the harder-to-retrieve memory of the non-errors of word1+ C-initial word2s (such as [mepeku] with the underlying forms /meʃ/+/peku/) which have not entered in their error archive in the first block. Overall, these predictions from the point of view of the ideal and suboptimal learner were not borne out, since the results reviewed so far in both of the tasks does not match the order in the predicted outcomes. 89 Table 5-8. Predictions and results of lexical indexation and constraint cloning Prediction Results Task – Item type Alt1st, NonAlt1st > Mix + NonAlt1st > Alt1st ❌ ❌ Mix > NonAlt1st Alt1st > NonAlt1st* Mix > Alt1st* (*nearly significant) Judgement – item NonA Judgement – item NonA Novel Segmentation – itemAlt Same as the previous subsections, examining the possible combinations of trial type accuracy rates is necessary to understand the similarities and differences among conditions better. To indicate that the constraint cloning has been successfully learned, while a high, above-chance accuracy for the alternating items (itemAlts) was essential, it was important that at the same time the accuracy for itemNonAlts was also above chance. Two examples of the itemNonAlt subtypes (3-4) were reviewed in the previous section. The itemAlts consist of two subtypes of errors similar to the itemNonAlts. The first subtype of the alternating items (n=3 familiar+1 heldout) is the choice between the two allomorph forms + C-initial word2s as can be seen from the tableau (5) below with the example stimuli [mebudol] vs [meʃbudol]. (5) /meʃ # budol/ NOC.C-L MAX NOC.C ☞ a. [me.budol] * b. [meʃ.budol] * * By choosing the suboptimal candidate [meʃbudol] participants would be making an error, which could be due to three possibilities: a. The learners know the correct underlying representation but they have not learned the correct ranking, but instead have a ranking where MAX outranks NOC.C-L; b. The learners have learned the correct ranking as above partially (MAX >> NOC.C) but failed to correctly clone the indexed constraint, or they have not learned that the /meʃ/ is part of the -L indexed lexicon; c. They have not learned the correct UR for /meʃ/ and think the UR form is actually /me/. The second subtype of the alternating items (n=3 familiar + 1 heldout) is the choice between the two allomorphs + V-initial word2s which can be seen in the tableau (6) below with 90 the example stimuli [ditugæʃ] vs [diugæʃ] given the correct underlying representation /dit/ has been posited. (6) /dit # ugæʃ/ MAX NOV.V ALIGN-L NOC.C ☞ a. [di.tugæʃ] * b. [di.ugæʃ] * * The errors in these subitems could be due to two possible reasons: a. The learners have learned the correct underlying representation but have not learned the correct ranking, but instead have a ranking where ALIGN-L outranks the faithfulness constraint MAX; b. The second reason could be due to a wrong UR, that is /di/ instead of /dit/. It is worth mentioning that all the itemB-A or itemB-NA trials in the judgement task included the choice between an optimal candidate and a harmonically bounded candidate as exemplified in the tableau (7) below for the [dikisɑ] vs [diʃkisɑ] trial. (7) /dit # kisɑ/ NOC.C-L MAX DEP NOC.C ☞ a. [di.kisɑ] * b. [diʃ.kisɑ] * * * * Since the suboptimal candidate in these trials is harmonically bounded, logically only not storing the correct representations would result in an error. For instance, in the example (7) the suboptimal candidate is violating the same markedness constraint as the one in example (5) but it even includes an unfaithful output besides the other violation. The majority of the participants in the three conditions responded to all the itemB-A and itemB-NA with high accuracy therefore, I do not include them in the discussion of the differences between conditions. In fact, as pointed out in Section 3.5 these items were a pre-set criterion to filter participants out from the whole analysis. This decision was made on the basis that incorrect choices on these items indicate the extreme outlier participants because such participants have not even tracked static co-occurrence restrictions such as *diʃ and *met. Choosing an incorrect underlying representation on this ground would be totally unmotivated and an error of a different nature. It is probably that this error could have arisen from not paying attention to the experimental stimuli and learning the phonotactic distributions rather than from a universal bias in favor of a particular segmentation in the face of ambiguities. 91 As can be seen from the itemAlt example tableaux (5‒6), the reasons for making errors on these subtypes are somewhat similar to the itemNonAlts (3‒4). Therefore, by dividing the testing trials itemAlt and itemNonAlt in the judgement task by their word2, Table 5-9 shows the possible combinations of the trial types accuracy schematically along with their interpretations. The “correct/incorrect” status indicates highly accurate/inaccurate responses. Table 5-9. Judgement task - schema of possible interpretations based on trial types C-initial Word2 + [me], [di] and /kɑn/ V-initial Word2 + [dit], [meʃ] and /lu/ Interpretation a. correct correct learned the end state grammar (the cloned constraints and the correct URs) b. correct incorrect learned the NoC.C-L >> Max >> NoC.C constraint ranking, but did not learn the crucial rankings of Dep >> NoV.V or Max >> Align-L or they did not learn the URs correctly c. incorrect correct learned the Dep >> No V.V and Max >> Align-L, but did not learn the NoC.C-L >> Max >> NoC.C or they did not learn the URs correctly d. incorrect incorrect cannot distinguish the alternating and non-alternating word1s or they did not learn the URs correctly To evaluate the results based the possible interpretations above, the descriptive mean accuracy of participant means23 in the three conditions is given in Table 5-10. With regards to learning the constraint cloning to address the inconsistency, it seems that participants in none of the conditions belong to row (a) in Table 5-9; rather they are closer to the results in (b) where the responses are more accurate in C-initial word2 trials compared to V-initial ones. The original prediction that the participants in the ordered conditions would perform better than the participants in the unordered condition was based on the hypothesis that the mechanism to clone constraints in two different blocks would be more difficult. Instead, the participants that seem to have been the least successful in coping with the NOC.C-L >> MAX >> NOC.C part of the constraint hierarchy are the NonAlt1st condition because they have the highest accuracy with alternating word1s + C- 23 Descriptive statistics is used here since the grouping of trials based on word2 was not the levels incorporated in the variables in the statistical model. 92 initial word2s and the lowest accuracy with non-alternating word1s + C-initial word2s. The 0.13 differences in means between the Mix and NonAlt1st within itemNonAlts of this subtype illustrates how they were significantly different in this task. The accuracy rate of 0.72 and below for V-initial word2s could be due to several possibilities. On the one hand, all the participants, regardless of their condition, seem to find the /lu/ + V-initial word2 trials challenging. This could be related to an incorrect underlying representation of the word2. The results reviewed previously in the segmentation tasks also reflect a similar challenge where the word2s in phrases such as /meʃibud/ were segmented as /ʃ/-initial more often than V-initial. However, on the other hand, if the wrong segmentation leading to an incorrect underlying representation was the only reason of their errors consistently, the results must have shown an asymmetry in accuracy compared with the alternating word1s + V-initial word2s such as the example in [ditugæʃ]. If the incorrect underlying representations of the word2s were all C-initial such as /tugæʃ/ then the accuracy in these items must have been as high as the C-initial word2 trials. Instead, the accuracy on these trials is somewhere between the trials such as [luæte] and [mebudol] for all participants. This suggests that the difficulty of these trials was not equal for all participants, and might have been due to a mix of different reasons. With respect to the differences between the error types reflecting different quality of their learning trajectory, participant in the Alt1st condition seem to have high accuracy with itemAlt trials, however the NonAlt1st participants have a lower accuracy rate with itemNonAlt trials which does not mirror the same pattern. Table 5-10. Average accuracy in itemNonAlt and itemAlt trials in the Judgement task 4 subtypes (each n=4) example (W ~ L) Alt1st NonAlt1st Mix [di], [me] + C-initial [mebudol] ~ [meʃbudol] 0.82 0.86 0.85 /kan/ + C-initial [kɑndʒomet] ~ [kɑdʒomet] 0.84 0.74 0.87 [dit], [meʃ] + V-initial [ditugæʃ] ~ [diugæʃ] 0.72 0.65 0.69 /lu/ + V-initial [luæte] ~ [luʃæte] 0.57 0.54 0.63 To speculate about the trajectories of each condition and their effects on learning the inconsistency some points can be taken from these results from a cognitive perspective. Firstly, in the predictions of the current study the Mix condition was not expected to be more successful than other conditions on any of the learning components in our predictions in Section 2.5.4. However, based on Table 5-10, the fact that these participants outperform the ordered conditions with a relatively big difference, exactly on those items that the participants of the two ordered conditions 93 were trained on in their first block, seems to suggest that this could be related to the trajectory of this condition in ways that we have not considered in our rationale. The nature of the difference between the items the participants in the two ordered conditions received compared to the unordered condition could have led to a memory boost for the Mix condition when recognizing the items during the testing subconsciously and therefore performing better on them. It is also possible that as we have discussed in Section 5.2.1. the segmentation of word2 has been less difficult for them. Lastly, one other possibility is that the hypothesis about the difficulty of resolving inconsistency needs to be adjusted. We might rather consider that it is easier to clone a constraint and index the lexicon in two blocks than to clone a constraint in one block with batch evidence from errors. Secondly, the Alt1st outperforming the NonAlt1st condition in the judgement task could lend itself to an interpretation about the cognitive effect of the order of learning lexically-specific properties and generalizations in a system along the lines of the simplicity framework as developed in Hsu and Chater (2010) and experiments of Wonnacott et al. (2017). In this framework, arguments about language learnability can be explicit and quantified. In order for a system to be learnable, there needs to be a trade-off between the cost of encoding the rules of a grammar and encoding all the individual observed items. Simpler grammars bear lower costs, however if the grammar requires too many exceptions and becomes complicated then it is worth investing in encoding more accurate individual lexical items. A conceptual evaluation of the two learning trajectories according to this framework seems to show that the learning trajectory of the Alt1st condition could be less costly. Learning a simple generalization motivated by the phonological grammar prior to the individual exceptions in the non-alternating items overloads the cost trade-off in their favour. However, the NonAlt1st learning trajectory starts with the lexically-specific aspect of the mini-language as learning the non-alternating word1s could be equivalent to encoding the language-specific lexical items where there is no single rule to be learned which would apply to both of them. This trajectory in comparison seems more costly. In the next subsection the effect of segmentation bias on the performance of participants is discussed in more detail. 5.3. Pilot experiment and the universal biases in segmentation In Section 2.3 example (7), the key components that an ideal learner must acquire along its path to master the allomorphy patterns for a morpheme are introduced. The first essential logical component identified for learning morpheme-specific alternations is understanding the semantic content of a phrase, which can inform the learner whether the phrase is mono-morphemic. We can argue based on the evidence of the results obtained that the next step in learning is to recognize 94 word boundaries. However, before discussing the implications of the experimental results for an account of morpho-phonological learning, it is important to consider the nature of the learning data used in the experiment and its ecological validity. In real-world language acquisition, children's learning input consists of adult output forms, which notably lack explicit segmentation or semantic information. The experimental setting mirrors real-world learning in that both contexts require the detection of morpheme boundaries. Discovering morpheme boundaries is closely linked to learning segmentation and semantic information. Participants in this artificial language learning experiment receive input data devoid of any segmentation information; however, they have access to additional contextual semantic cues. In this regard, their knowledge of semantics is controlled for, as compared to children, they are informed from the outset that they will be learning about phrases containing two words that correspond to the two images displayed on the screen. As we have discussed in the previous subsections, participants in the experiment did not perform as well in the word segmentation tasks as in the phrase judgement task. The tension between universal constraints and language-specific patterns is one of the key challenges that is present for the acquisition of liaison developmentally speaking, as we have discussed in Section 2.4.1. Throughout the testing trials of the current artificial language learning experiment with adults, the effect of the universal constraints that favor the alignment of syllable structure and word boundaries can also be clearly observed among all conditions. The results show that the testing trials that involve any ambiguous segmentation due to resyllabification of the two morphemes consistently have lower accuracy rates than other types of trials. This decrease of accuracy appeared in the novel segmentation task with itemAlts such as [ditogi] - /ogi/ vs /togi/ and itemNonAlts such as [kɑneʃin] - /eʃin/ vs /neʃin/, as well as one type of judgment task with [luæte] vs [luʃæte] where the V-initial word2 /æte/ could have been parsed as C-initial /ʃæte/. Using evidence of phrases that contain a word1 of the "non-alternating" type such as [kɑ.ne.ʃin] and [kɑn.bu.dol] could lead to participants learning that ALIGN-L is a violable constraint and that the underlying representation of the word1 is /kɑn/. Overcoming this universal bias by realizing that the constraint needs to be demoted has an important effect because it is a pre-requisite knowledge that could ideally unlock the path to learning the alternations. To highlight the persistent strong effect of the universal markedness constraint, ALIGN-L, I draw on the results from a pilot version of the experiment. In the pilot round of this experiment, unlike the current version, all the training items were fully randomized within each block and the number of training trials was lower. Figure 5-1 shows the accuracy in task 2, the familiar segmentation task and Figure 5-2 shows task 3, the novel segmentation task. In each side-by-side comparison, the box and whiskers on the right side are from the pilot experiment and the box and whiskers on the left are from the current experiment. The result of the pilot experiment plotted for the segmentation tasks illustrate the below chance or near chance accuracy for the itemAlts (top-95 leftmost facet of both Figures) and itemNonAlts (the top-rightmost facet of Figure 5-2) in the three conditions. Figure 5-1. Pilot vs current experiment in the familiar segmentation task In the familiar segmentation task (Figure 5-1), the differences between the pilot and the current experiment can be summarized in two ways. All participants seem to perform well on C-initial word2s (itemB-A) in both versions. However, participants in the Mix condition seem to perform differently on V-initial word2s (itemAs) than the other conditions in the current experiment. Focusing on the right set of box and whiskers in the left facet, the median accuracy of the Mix is close to 0.5 in the current experiment in contrast to being at the floor in the pilot. In the novel segmentation task, the differences in performance between the current experiment and the pilot seem to be among V-initial word2s (itemAlt and itemNonAlt) as well. 96 In the pilot version of the experiment, the number of participants was smaller and there were a few other changes. Therefore, a detailed statistical comparison would not be appropriate. However, it is interesting to compare the effect of the full randomization of the training stimuli with the pseudo-randomization. The pseudo-randomization order we have implemented in the current experiment is similar to the idea of a contrastive paradigm suggested by Tesar (2014: 247). Specifically, the idea is that the same V-initial noun in different contexts can facilitate the learning of alternation, such as encountering /ogi/ in the contexts of [ditogi] and [meʃogi] one after the other. As these two plots show, within the itemAlts in both tasks and itemNonAlts, the condition that seems to have been affected more consistently by the switch to the contrastive paradigm in the training trials is the Mix condition. As we have discussed before, the higher accuracy of the Mix condition in learning the allomorphy and the alternation was not part of the initial predictions of the study, therefore further research is needed to confirm whether the contrastive paradigm only benefits the Mix condition in terms of learning the language-specific demands for segmentation or whether it also extends to learning the morpheme-specific alternation as well. Figure 5-2. Pilot vs current experiment in the novel segmentation task 97 Overall, even though the contrastive paradigm in the training trials seem to have alleviated some of the confounding effects of the pressure under the universal constraints to ensure participants learn the language-specific patterns more efficiently, the results are not conclusive. There is still high variation among participants possibly due to intra-participant differences which prevents the effect of the different trajectories from being observed more clearly. The written feedback collected at the end of the experiment from participants also reflect this situation. It is generally known that not all participants perform equally well in artificial language learning experiments; some might be more focused on the task and others might struggle more with the cognitive load and memory issues (Moreton and Pertsova, 2023; Moreton et al., 2021; McMullin, 2016). The next section discusses the analysis of the data which focuses on the results of the subset of participants, who are referred to as “successful” learners in the artificial language learning literature, to gain some insight into the factors that contribute to successful learning of this mini language. 5.4. Analysis of the subset of successful learners To analyze the results further, I targeted the subset of participants whose overall accuracy was above a certain threshold showing above-chance level of accuracy. Following the literature of artificial language learning studies (McMullin, 2016; Martin and White, 2021) the threshold was defined using a binomial right-tailed test. In other words, to be included in the subset of successful learners, the participants must have an accuracy rate above 0.69 (23 or more correct trials out of 32 trials) which is above the minimum proportion that differs significantly from chance-performance according to a right-tailed binomial test at an alpha level of 0.05. The first judgement task was analyzed separately (n=32 trials) and the second task and the third task which were both segmentation tasks were collapsed together (n=32 trials). The different proportions of the subset of successful learners in different tasks are shown in Table 5-11. In the judgement task, over 85% of the participants achieved success, while in the segmentation task, only 21% were successful. This stark contrast in the proportions of successful learners across the two tasks highlights that all participants were affected by segmentation biases stemming from outside the training phase. An interesting takeaway from this analysis could still lie in comparing the proportions of successful learners despite this bias. Among the three conditions, the subset of successful learners in the Mix condition was the largest in the segmentation task, with 33% of participants. The distribution of the 39 learners who had above-chance accuracy in all tasks are plotted first for the phrase judgement task in Figure 5-3. 98 Table 5-11. The proportion of the successful learners to all participants Alt1st NonAlt1st Mix Total All participants 71 66 61 201 Successful - Phrase judgement task 83% (59) 83% (55) 93% (57) 85% (171) Successful -Segmentation tasks 13% (9) 20% (13) 33% (20) 21% (42) Successful - all tasks 13% (9) 18% (12) 29% (18) 19% (39) Figure 5-3 indicates that the distributions across the conditions are similar both across and within trial types. On itemNonAlt trials, when considering all learners, a statistically significant difference exists among the Mix and Alt1st conditions. However, the accuracy in the NonAlt1st condition is higher in subset of successful learners compared to all participants, while the accuracy of the Mix is similar in both side-by-side box and whisker plots. A logistic regression model was applied to the subset of successful learners from both the judgment and segmentation tasks. The emmeans pairwise comparisons revealed that in Task1’s itemNonA, there was a significant difference between the Alt1st and NonAlt1st condition. The results of the comparisons can be found in the Appendix (Bx). Given the reduced number of participants in the segmentation task and the imbalance between the participants in the two groups of learners being compared, the regression model outputs are not comparable to previous models. 99 Figure 5-3. Subset of the successful learners vs. all learners in task 1 (phrase judgement) The distribution of the successful learners (in all tasks) is plotted by the three conditions across the three item types in Figures 5-4 and 5-5. The distributions of the conditions are similar both across and within itemB-A trial types. Within the itemAlt trials participants in the three conditions have below chance performance in all learners, but that is not the case anymore when considering the successful learners. Also, especially considering the comparison of the side-by-side box and whiskers in Figure 5-5, there seems to be a difference among the error distributions within each condition according to the prediction which stated that the participants in the Alt1st condition are more accurate with itemAlts and the participants in the NonAlt1st condition are more accurate with the itemNonAlt. 100 Figure 5-4. Subset of the successful learners vs. all learners in task 2 (familiar segmentation) The more intriguing aspect of this discussion lies in whether any of the conditions can more effectively generalize their learning to novel items, as illustrated in Figure 5.5. The pairwise emmeans comparisons did not show any significant differences in task 3. The full results can be found in Appendix B5. However, judging based on the descriptive statistics (such as variation and mean values) among the conditions, it appears that differences in the ability to generalize to novel items for participants in different conditions depends on the type of item. Notably, the Alt1st condition shows a ceiling effect in its ability to generalize what has been learned to novel itemAlts, while both the NonAlt1st and Mix conditions reach ceiling performance within novel itemNonAlts. These findings indicate that the trajectory of the Alt1st group differs qualitatively from the other two groups, at least within the limited sample size of successful learners. 101 Figure 5-5. Subset of the successful learners vs. all learners in task 3 (novel segmentation) 5.5. Analysis of the effect of segmentation accuracy on the phrase judgement task To analyze if performance on the segmentation tasks can be a predictor of participants performance on the phrase judgement task, I have included a continuous variable called “segmentation score” for each participant. The values for this variable were calculated for each participant as their rate of overall accuracy in the two segmentation tasks (n/32; not including their null responses). A logistic regression model was fitted with the following formula where condition, trial type and segmentation score were included as fixed effects. (10) responses ~ conditions + trials + segmentation score + (1 + trials|subject) + (1+ conditions|stimulus) 102 The results of the model summary show that a higher segmentation score significantly increases the probability of participant’s correct responses in the judgement task (β=2.1, SE=0.37, p=0). The likelihood ratio test comparing the model in (10) and a simpler model without the main effect of segmentation score was significant. Therefore, segmentation score is a predictor of accuracy in the judgment task. Two separate models were also considered one with the addition of the interaction of segmentation score and trial type and another one with the addition of the interaction of segmentation score and condition in the fixed effects. The interactions were included to investigate whether the relationship between response accuracy and segmentation score depends on the trial type or condition. However, a likelihood ratio test comparing these models simpler models without the interaction terms was not significant. More details about these models can be found in the Appendix B6. Regardless to visualize the effect of the segmentation score, the following plots in Figure 5-6 and Figure 5-7 illustrate these effects across the four trial types and three conditions. Figure 5-6. Predicted probabilities of a correct response in the judgement task by accuracy score in segmentation across trial types 103 The effect seems stronger in the itemNonAlts compared to itemAlts, as the degree of the positive slope in the probability of correct responses is slightly larger. This could be an indication that the variation in responses to itemNonAlt phrases such as choosing [luʃæte] over [luæte] could have been due to the difficulties in segmentation. Similarly, among conditions, as shown in Figure 5-7 below, the variation in the responses seems to be correlated with the participant’s segmentation accuracy. This effect seems slightly stronger in Alt1st compared to the other ordered condition, NonAlt1st. 5.6. Conclusion and future work The study of the learnability of interface phenomena has proven increasingly valuable, as it enhances our understanding of fundamental theoretical concepts such as representations and the modular knowledge of grammar, as well as implications for language acquisition and linguistic disorders. However, many experimental studies on morpho-phonological learning face challenges due to the complex interactions among different grammatical modules that need to be integrated. This research has focused on the effect of learning trajectories on learning French liaison, where syntactic, semantic, and morphological knowledge interact with phonological grammar. Preliminary results suggest that input data and learning trajectories influence participants' performance only when tested with full phrases in a forced-choice tasks. However, more research is certainly needed to confirm the predictions regarding the differential learning of different trajectories, as obtaining conclusive results to reject the null hypotheses has not been possible. Figure 5-7. Predicted probabilities of a correct response in the judgement task by accuracy score in segmentation across conditions 104 The findings indicate that in an experimental setting controlling for syntactic and semantic information, adult learners achieve above-chance accuracy rates in judgment tasks involving word1+word2 phrases. However, when presented with phrases including novel nouns and even phases with familiar nouns, their accuracy in word segmentation falls below chance levels. Moreover, the representational challenges observed in the segmentation errors of French-speaking children (Babineau et al., 2023; Buerkin-Pontrelli et al., 2017; Chevrot et al., 2009) similarly affect adult learners in our artificial language study. In Buerkin-Pontrelli et al. (2017) experimental study, when asked to use novel V-initial word2s such as /ivak/ in a liaison-triggering context, children’s errors involved replacement or insertions (e.g., deux + /n-ivak/) whereas adults’ errors involved omission of the liaison consonant more frequently. In the current study, adult participant errors were similar to those “/n-ivak/” errors of children in that when provided with the opportunity to judge or segment phrases containing V-initial words they chose to fill the onset position to create C-initial or CV.CV(C) word2 forms. These results underscore the intricate interplay between the essential layer of morphological information and phonological learning, which may have obscured the effects of other challenging aspects of learning we originally aimed to investigate. Despite these complexities, learners of French successfully attain the end-state grammar and ultimately master morpheme-specific patterns. Recent studies indicate that as early as 24 months of age, toddlers are able to parse novel V-initial words within variable contexts, leveraging their differential knowledge of liaison consonants (Babineau, et al., 2023; Babineau et al., 2021). Although this developmental journey could be prolonged, elicitation tasks show that by age 3 children are on their way to adult-like representations (Buerkin-Pontrelli et al., 2017). Bearing in mind that children at a very young age are to some extent reaching adult level of performance in experimental contexts, in what ways could the current artificial language learning experiment shed light on the extent to which various learning dimensions emerging from the data are less challenging than expected, or in other words more “learnable” than others? One of the experimental conditions in the current study, the unordered condition (Mix), is analogous to children’s learning data because they both include a variety of different phrases including both alternating and non-alternating word1s from the start. As the results in Section 5.4 show, the proportion of successful learners in the current study who were trained with incremental inconsistencies present within two blocks (Mix condition) was greater than the proportion of successful learners trained on inconsistencies present between two separate blocks(29% vs 12% and 8%). Therefore, the implication of these results for a theory of learnability suggests that tackling inconsistencies could be less challenging than expected and that it seems to have been modulated by learning trajectory. On the other hand, challenges associated to overcoming the difficulties of segmenting V-initial word2s affect all participants equally and are of a different nature. Although, future research is essential to deepen our understanding of these two factors. 105 In the domain of artificial language learning experiments, significant inter-participant variability and discrepancies in learning outcomes are frequently observed (Moreton and Pertsova, 2023; McMullin, 2016). Consequently, an effective strategy for future research would be to replicate the study and to increase the participant population. It is also interesting to undertake a comparative analysis between various learner types to study the variation among learners. This approach would allow for the comparison of strategies used in learning between a subset of participants who consistently demonstrate an accurate versus those with inaccurate learning outcome throughout the testing phase. To enhance the robustness of the findings, one suggestion is to replicate the experiments utilizing different variations of the experimental stimuli avoiding confounding effects. This could involve the creation of phrase structures beyond possessive phrase forms, such as the current “proper noun + everyday object” configuration, as well as the incorporation of V-initial word1 forms into the experimental design. The latter is to introduce greater diversity in word shapes within the artificial language with V-initial phrases. On a separate note, in order to investigate the impact of the order of allomorphs in relation to nouns more effectively, a novel artificial language could be designed that positions allomorphs post-nominally, in contrast to the pre-nominal allomorphs in the current study. To more accurately discern the influence of recency in memory, an intermittent testing phase could be introduced between the two training blocks. However, in forced-choice tasks, the choice that is being compared with the intended optimal candidate could potentially be a form of negative learning data. It is important, therefore, to adopt an alternative testing methodology rather than forced-choice testing, in order to mitigate the effects arising from exposure to negative data amidst training. Furthermore, to explore age-related differences in learning strategies, it would be beneficial to conduct a similar version of the experiment with younger participants, who possess less meta-linguistic knowledge and linguistic experience, and to analyze their strategies and errors across different developmental stages. Experimental studies’ advantages outweigh their disadvantages. While experimental settings often pose challenges in examining aspects of morpho-phonological learning, such as cognitive load and limited learning durations, the unique controlled nature of these experiments continues to offer valuable insights into the mechanisms of learning. 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Phonotactics and morphophonology in early child language: Evidence from Dutch. Applied Psycholinguistics, 33(3), 481–499. https://doi.org/10.1017/S0142716411000440 114 Appendices Appendix A. Stimuli lists List of Training Trials Word1 Word2 Word1 Type Phrase dit æte Alternating Word1 dit ɑtæl Alternating Word1 meʃ ɑtæl Alternating Word1 me budol Alternating Word1 di dʒomet Alternating Word1 me dʒomet Alternating Word1 meʃ edæp Alternating Word1 di gɑbiʃ Alternating Word1 me gɑbiʃ Alternating Word1 dit ibud Alternating Word1 di kisɑ Alternating Word1 me kisɑ Alternating Word1 me mæti Alternating Word1 meʃ ogi Alternating Word1 di pæzɑm Alternating Word1 me peku Alternating Word1 dit ufe Alternating Word1 meʃ ufe Alternating Word1 dit ugæʃ Alternating Word1 meʃ ugæʃ Alternating Word1 di vezu Alternating Word1 lu æte NonAlternating Word1 kɑn ɑtæl NonAlternating Word1 lu ɑtæl NonAlternating Word1 kɑn budol NonAlternating Word1 kɑn dʒomet NonAlternating Word1 lu dʒomet NonAlternating Word1 kɑn edæp NonAlternating Word1 kɑn gɑbiʃ NonAlternating Word1 lu gɑbiʃ NonAlternating Word1 115 lu ibud NonAlternating Word1 kɑn ido NonAlternating Word1 lu ido NonAlternating Word1 kɑn kisɑ NonAlternating Word1 lu kisɑ NonAlternating Word1 kɑn mæti NonAlternating Word1 kɑn ogi NonAlternating Word1 lu pæzɑm NonAlternating Word1 kɑn peku NonAlternating Word1 lu peku NonAlternating Word1 kɑn ufe NonAlternating Word1 lu ufe NonAlternating Word1 kɑn ugæʃ NonAlternating Word1 lu ugæʃ NonAlternating Word1 lu vezu NonAlternating Word1 List of Training Trials (held-out phrases that do not appear in training) Word1 Word2 Word1 Type Phrase meʃ æte Alternating Word1 di budol Alternating Word1 dit edæp Alternating Word1 meʃ ibud Alternating Word1 dit ogi Alternating Word1 me pæzɑm Alternating Word1 me vezu Alternating Word1 kɑn æte NonAlternating Word1 lu budol NonAlternating Word1 lu edæp NonAlternating Word1 kɑn ibud NonAlternating Word1 di mæti NonAlternating Word1 lu mæti NonAlternating Word1 lu ogi NonAlternating Word1 kɑn pæzɑm NonAlternating Word1 kɑn vezu NonAlternating Word1 116 Testing trials – Task 1 Phrase Judgement Correct Choice Incorrect Choice Trial Type Item Familiarity luibud luʃibud itemNonAlt familiar luedæp luʃedæp itemNonAlt held-out luæte luʃæte itemNonAlt familiar luogi luʃogi itemNonAlt held-out kɑngɑbiʃ kɑgɑbiʃ itemNonAlt familiar kɑndʒomet kɑdʒomet itemNonAlt familiar kɑnkisɑ kɑkisɑ itemNonAlt familiar kɑnpeku kɑpeku itemNonAlt familiar meʃedæp meʃtedæp itemB-A familiar ditido ditʃido itemB-A familiar dikisɑ diʃkisɑ itemB-A familiar memæti metmæti itemB-A familiar dipeku diʃpeku itemB-A familiar ditufe ditʃufe itemB-A held-out meʃæte meʃtæte itemB-A familiar mevezu metvezu itemB-A held-out lupæzɑm lutpæzɑm itemB-NA familiar lubudol lutbudol itemB-NA familiar luvezu lutvezu itemB-NA familiar lumæti lutmæti itemB-NA familiar kɑnɑtæl kɑɑtæl itemB-NA familiar kɑnugæʃ kɑugæʃ itemB-NA familiar kɑnufe kɑufe itemB-NA held-out kɑnido kɑido itemB-NA held-out ditɑtæl diɑtæl itemAlt familiar mebudol meʃbudol itemAlt familiar didʒomet ditdʒomet itemAlt familiar digɑbiʃ ditgɑbiʃ itemAlt familiar meʃogi meogi itemAlt familiar ditugæʃ diugæʃ itemAlt familiar meʃibud meibud itemAlt held-out mepæzɑm meʃpæzɑm itemAlt held-out godoeves godoteves practice 117 godotnoros godonoros practice Testing trials – Task 2 Familiar Segmentation Phrase Prompt Correct Choice Incorrect Choice Trial Type Item Familiarity ditæte æte tæte itemAlt seen meʃɑtæl ɑtæl ʃɑtæl itemAlt seen ditibud ibud tibud itemAlt seen meʃido ido ʃido itemAlt seen meʃufe ufe ʃufe itemAlt seen meʃugæʃ ugæʃ ʃugæʃ itemAlt seen ditedæp edæp tedæp itemAlt unseen ditogi ogi togi itemAlt unseen ditæte æte tæte itemAlt seen meʃɑtæl ɑtæl ʃɑtæl itemAlt seen ditibud ibud tibud itemAlt seen meʃido ido ʃido itemAlt seen medʒomet dʒomet omet itemB-A seen megɑbiʃ gɑbiʃ ɑbiʃ itemB-A seen mekisɑ kisɑ isɑ itemB-A seen dipæzɑm pæzɑm æzɑm itemB-A seen mepeku peku eku itemB-A seen divezu vezu ezu itemB-A seen dibudol budol udol itemB-A unseen dimæti mæti æti itemB-A unseen medʒomet dʒomet omet itemB-A seen megɑbiʃ gɑbiʃ ɑbiʃ itemB-A seen bodominid minid inid practice bodoperem erem perem practice Testing trials – Task 3 Novel Segmentation Phrase Prompt Correct Choice Incorrect Choice Trial Type Item Familiarity meʃitʃæn itʃæn ʃitʃæn itemAlt novel meʃezɑ ezɑ ʃezɑ itemAlt novel ditɑjor ɑjor tɑjor itemAlt novel ditɑvi ɑvi tɑvi itemAlt novel 118 meʃitʃæn itʃæn ʃitʃæn itemAlt novel mefærus færus ærus itemB-A novel mefule fule ule itemB-A novel ditʃægef tʃægef ægef itemB-A novel disædʒɑ sædʒɑ ædʒɑ itemB-A novel lurunip runip unip itemB-NA novel luzoʃek zoʃek oʃek itemB-NA novel lurejɑ rejɑ ejɑ itemB-NA novel luvoli voli oli itemB-NA novel kɑnokɑn okɑn nokɑn itemNonAlt novel kɑneʃin eʃin neʃin itemNonAlt novel kɑnosu osu nosu itemNonAlt novel kɑnimɑ imɑ nimɑ itemNonAlt novel 119 Appendix B. Statistical summaries 1. Task1 - Phrase Judgement Logistic regression model: formula6_b1 <- responses ~ conditions + trials + familiarity + conditions * trials + conditions * familiarity + (1 + trials|subject) + (1+ conditions |stimulus) model6_b1 <- glmer(formula6_b1, data = data_s1, control=glmerControl(optimizer = "optimx", calc.derivs = FALSE, optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE)), family = binomial(link = "logit")) MODEL INFO: Observations: 6297 Dependent Variable: responses Type: Mixed effects generalized linear regression Error Distribution: binomial Link function: logit MODEL FIT: AIC = 5808.26, BIC = 6003.95 Pseudo-R² (fixed effects) = 0.05 Pseudo-R² (total) = 0.31 FIXED EFFECTS: ------------------------------------------------------------------ Est. S.E. z val. p ----------------------------------- ------- ------ -------- ------ (Intercept) 1.11 0.38 2.94 0.00 conditionsNA1 -0.48 0.21 -2.31 0.02 conditionsMix 0.18 0.17 1.10 0.27 trialsitemA 0.47 0.53 0.90 0.37 trialsitemBL_A 0.74 0.53 1.40 0.16 trialsitemBL_NA 1.12 0.53 2.10 0.04 familiarityheld-out 0.26 0.31 0.85 0.40 conditionsNA1:trialsitemA 0.21 0.30 0.70 0.48 conditionsMix:trialsitemA -0.30 0.25 -1.20 0.23 conditionsNA1:trialsitemBL_A 0.43 0.31 1.36 0.17 conditionsMix:trialsitemBL_A 0.00 0.26 0.01 0.99 conditionsNA1:trialsitemBL_NA 0.20 0.33 0.61 0.54 conditionsMix:trialsitemBL_NA -0.10 0.28 -0.35 0.73 ------------------------------------------------------------------ Emmeans contrast trial_type estimate SE z.ratio p.value A1 - NA1 itemNonA 0.48 0.21 2.31 0.06 120 itemA 0.27 0.24 1.13 0.78 itemBL_A 0.05 0.25 0.21 1.00 itemBL_NA 0.28 0.28 0.99 0.96 A1 - Mix itemNonA -0.18 0.17 -1.10 0.82 itemA 0.11 0.20 0.57 1.00 itemBL_A -0.19 0.22 -0.85 1.00 itemBL_NA -0.09 0.26 -0.34 1.00 NA1 - Mix itemNonA -0.67 0.21 -3.20 0.00 itemA -0.15 0.24 -0.66 1.00 itemBL_A -0.24 0.26 -0.93 1.00 itemBL_NA -0.37 0.29 -1.27 0.61 Chi-Square Anova tests 2 main effects (without condition) vs 3 main effects Models: model3_b1: responses ~ trial_type + familiarity + (1 + trial_type | subject) + (1 + conditions| stimulus) model4_b1: responses ~ conditions+ trial_type + familiarity + (1 + trial_type | subject) + (1 + conditions| stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model3_b1 21 5804.1 5945.8 -2881.1 5762.1 model4_b1 23 5800.7 5955.9 -2877.4 5754.7 7.3755 2 0.02503 * 2 main effects (without trials) vs 3 main effects Models: model2_b1: responses ~ conditions+ familiarity + (1 + trial_type | subject) + (1 + conditions| stimulus) model4_b1: responses ~ conditions+ trial_type + familiarity + (1 + trial_type | subject) + (1 + conditions| stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model2_b1 20 5806.8 5941.8 -2883.4 5766.8 model4_b1 23 5800.7 5955.9 -2877.4 5754.7 12.092 3 0.007074 ** 2 main effects (without familiarity) vs 3 main effects Models: model1_b1: responses ~ conditions+ trial_type + (1 + trial_type | subject) + (1 + conditions| stimulus) model4_b1: responses ~ conditions+ trial_type + familiarity + (1 + trial_type | subject) + (1 + conditions| stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model1_b1 22 5799.4 5947.9 -2877.7 5755.4 model4_b1 23 5800.7 5955.9 -2877.4 5754.7 0.6758 1 0.411 3 main effects (without interaction) vs with interaction Models: model4_b1: responses ~ conditions+ trial_type + familiarity + (1 + trial_type | subject) + (1 + conditions| stimulus) 121 model5_b1: responses ~ conditions + trials + familiarity + conditions * trials + (1 + trials | subject) + (1 + conditions | stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model4_b1 23 5800.7 5955.9 -2877.4 5754.7 model5_b1 29 5808.3 6003.9 -2875.1 5750.3 4.4784 6 0.6122 2. Task2 - Familiar segmentation Logistic regression model: formula5_b2 <- responses ~ conditions + trials + familiarity + conditions * trials + (1 + trials|subject) + (1+ conditions |stimulus) model5_b2 <- glmer(formula5_b2, data = data_s2, control=glmerControl(optimizer = "optimx", calc.derivs = FALSE, optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE)), family = binomial(link = "logit")) MODEL INFO: Observations: 3141 Dependent Variable: responses Type: Mixed effects generalized linear regression Error Distribution: binomial Link function: logit MODEL FIT: AIC = 2499.17, BIC = 2596.00 Pseudo-R² (fixed effects) = 0.42 Pseudo-R² (total) = 0.72 FIXED EFFECTS: ----------------------------------------------------------------- Est. S.E. z val. p ---------------------------------- ------- ------ -------- ------ (Intercept) -1.86 0.30 -6.16 0.00 conditionsNA1 0.21 0.44 0.47 0.64 conditionsMix 0.61 0.50 1.22 0.22 trialsitemBL_A 4.47 0.41 10.84 0.00 familiarityheld-out 0.17 0.17 1.00 0.32 conditionsNA1:trialsitemBL_A -0.10 0.61 -0.17 0.86 conditionsMix:trialsitemBL_A -0.17 0.71 -0.24 0.81 ----------------------------------------------------------------- Emmeans: contrast trial_type estimate SE z.ratio p.value A1 - NA1 itemA -0.21 0.44 -0.47 1.00 itemBL_A -0.61 0.50 -1.22 0.67 NA1 - Mix item_A -0.40 0.46 -0.87 1.00 itemBL_A -0.10 0.34 -0.31 1.00 A1 - Mix itemA -0.44 0.43 -1.03 0.90 122 itemBL_A -0.34 0.37 -0.89 1.00 ChiSquare Anova test: 2 main effects (without condition) vs 3 main effects model3_b2: responses ~ trials+ familiarity+ (1 + trials| subject) + (1 + conditions| stimulus) model4_b2: responses ~ conditions+ trials+ familiarity+ (1 + trials| subject) + (1 + conditions| stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model3_b2 12 2494.2 2566.9 -1235.1 2470.2 model4_b2 14 2495.2 2580.0 -1233.6 2467.2 3.0025 2 0.2229 2 main effects (without trial) vs 3 main effects Models: model2_b2: responses ~ conditions+ familiarity+ (1 + trials| subject) + (1 + conditions| stimulus) model4_b2: responses ~ conditions+ trials+ familiarity+ (1 + trials| subject) + (1 + conditions| stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model2_b2 13 2548.2 2626.9 -1261.1 2522.2 model4_b2 14 2495.2 2580.0 -1233.6 2467.2 54.995 1 1.209e-13 *** 2 main effects (without familiarity) vs 3 main effects Models: model1_b2: responses ~ conditions+ trials+ (1 + trials| subject) + (1 + conditions| stimulus) model4_b2: responses ~ conditions+ trials+ familiarity+ (1 + trials| subject) + (1 + conditions| stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model1_b2 13 2494.1 2572.8 -1234.1 2468.1 model4_b2 14 2495.2 2580.0 -1233.6 2467.2 0.9062 1 0.3411 3 main effects (without interaction) vs with interaction Models: model4_b2: responses ~ conditions+ trials+ familiarity+ (1 + trials| subject) + (1 + conditions| stimulus) model5_b2: responses ~ conditions + trials + familiarity + conditions * trials + (1 + trials | subject) + (1 + conditions | stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model4_b2 14 2495.2 2580 -1233.6 2467.2 model5_b2 16 2499.2 2596 -1233.6 2467.2 0.0597 2 0.9706 3. Task 3 - Novel segmentation Logistic regression model: MODEL INFO: 123 Observations: 3146 Dependent Variable: responses Type: Mixed effects generalized linear regression Error Distribution: binomial Link function: logit MODEL FIT: AIC = 2665.30, BIC = 2834.81 Pseudo-R² (fixed effects) = 0.37 Pseudo-R² (total) = 0.74 FIXED EFFECTS: ------------------------------------------------------------------ Est. S.E. z val. p ----------------------------------- ------- ------ -------- ------ (Intercept) -1.15 0.33 -3.47 0.00 conditionsNA1 0.46 0.50 0.92 0.36 conditionsMix 0.99 0.49 1.99 0.05 trialsitemA -1.72 0.34 -5.11 0.00 trialsitemBL_A 4.04 0.51 7.90 0.00 trialsitemBL_NA 3.51 0.44 7.93 0.00 conditionsNA1:trialsitemA -0.04 0.52 -0.08 0.93 conditionsMix:trialsitemA 0.48 0.50 0.96 0.34 conditionsNA1:trialsitemBL_A -0.19 0.77 -0.25 0.80 conditionsMix:trialsitemBL_A -0.83 0.77 -1.08 0.28 conditionsNA1:trialsitemBL_NA -1.19 0.67 -1.79 0.07 conditionsMix:trialsitemBL_NA -1.04 0.66 -1.57 0.12 ------------------------------------------------------------------ Emmeans: contrast trial_type estimate SE z.ratio p.value A1 - NA1 itemNonA -0.46 0.50 -0.92 1.00 itemA -0.42 0.63 -0.66 1.00 itemBL_A -0.27 0.50 -0.53 1.00 itemBL_NA 0.73 0.35 2.11 0.10 A1 - Mix itemNonA -0.99 0.49 -1.99 0.14 itemA -1.46 0.62 -2.35 0.06 itemBL_A -0.16 0.49 -0.31 1.00 itemBL_NA 0.06 0.35 0.16 1.00 NA1 - Mix itemNonA -0.53 0.50 -1.05 0.88 itemA -1.05 0.62 -1.68 0.28 itemBL_A 0.11 0.50 0.22 1.00 itemBL_NA -0.68 0.33 -2.05 0.12 124 ChiSquare Anova test: 1 main effect (without condition) vs 2 main effects Models: model3_b3: responses ~ trials + (1 + trials | subject) + (1 + conditions | stimulus) model4_b3: responses ~ conditions + trials + (1 + trials | subject) + (1 + conditions | stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model3_b3 20 2664.8 2785.8 -1312.4 2624.8 model4_b3 22 2661.7 2794.8 -1308.8 2617.7 7.121 2 0.02843 * 1 main effects (without item) vs 2 main effects Models: model2_b3: responses ~ conditions + (1 + trials | subject) + (1 + conditions | stimulus) model4_b3: responses ~ conditions + trials + (1 + trials | subject) + (1 + conditions | stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model2_b3 19 2723.3 2838.3 -1342.7 2685.3 model4_b3 22 2661.7 2794.8 -1308.8 2617.7 67.675 3 1.343e-14 *** 2 main effects (without interaction) vs with interaction Models: model4_b3: responses ~ conditions + trials + (1 + trials | subject) + (1 + conditions | stimulus) model5_b3: responses ~ conditions + trials + conditions * trials + (1 + trials | subject) + (1 + conditions | stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model4_b3 22 2661.7 2794.8 -1308.8 2617.7 model5_b3 28 2665.3 2834.8 -1304.7 2609.3 8.3503 6 0.2135 4. Task 2 and 3 - Both segmentation tasks Logistic regression model: formula5_b4 <- responses ~ conditions + trials_sw + conditions * trials_sw + familiarity + (1 + trials|subject) + (1+ conditions|stimulus) model5_b4 <- glmer(formula5_b4, data = data_s4, control=glmerControl(optimizer = "optimx", calc.derivs = FALSE, optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE)), family = binomial(link = "logit")) MODEL INFO: Observations: 6287 Dependent Variable: responses Type: Mixed effects generalized linear regression Error Distribution: binomial Link function: logit 125 MODEL FIT: AIC = 4970.83, BIC = 5132.73 FIXED EFFECTS: ------------------------------------------------------------- Est. S.E. z val. p ------------------------------ ------- ------ -------- ------ (Intercept) 2.58 0.22 11.73 0.00 conditionsNA1 -0.13 0.27 -0.48 0.63 conditionsMix 0.22 0.28 0.77 0.44 trials_swV -4.23 0.40 -10.47 0.00 familiarityheld-out 0.12 0.25 0.46 0.65 familiaritynovel -0.14 0.17 -0.84 0.40 conditionsNA1:trials_swV 0.35 0.57 0.60 0.55 conditionsMix:trials_swV 0.53 0.59 0.90 0.37 ------------------------------------------------------------- ChiSquare Anova test: 2 main effects (without condition) vs 3 main effects Models: model3_b4: responses ~ trials_sw + familiarity + (1 + trials | subject) + (1 + conditions | stimulus) model4_b4: responses ~ conditions + trials_sw + familiarity + (1 + trials | subject) + (1 + conditions | stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model3_b4 20 4969.4 5104.3 -2464.7 4929.4 model4_b4 22 4967.6 5116.1 -2461.8 4923.6 5.7478 2 0.05648 . 2 main effects (without item) vs 3 main effects Models: model2_b4: responses ~ conditions + familiarity + (1 + trials | subject) + (1 + conditions | stimulus) model4_b4: responses ~ conditions + trials_sw + familiarity + (1 + trials | subject) + (1 + conditions | stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model2_b4 21 5058.0 5199.7 -2508.0 5016.0 model4_b4 22 4967.6 5116.1 -2461.8 4923.6 92.368 1 < 2.2e-16 *** 2 main effects (without familiarity) vs 3 main effects Models: model1_b4: responses ~ conditions + trials_sw + (1 + trials | subject) + (1 + conditions | stimulus) model4_b4: responses ~ conditions + trials_sw + familiarity + (1 + trials | subject) + (1 + conditions | stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model1_b4 20 4964.9 5099.8 -2462.4 4924.9 model4_b4 22 4967.6 5116.1 -2461.8 4923.6 1.2368 2 0.5388 3 main effects (without interaction) vs with interaction 126 Models: model4_b4: responses ~ conditions + trials_sw + familiarity + (1 + trials | subject) + (1 + conditions | stimulus) model5_b4: responses ~ conditions + trials_sw + conditions * trials_sw + familiarity + (1 + trials | subject) + (1 + conditions | stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model4_b4 22 4967.6 5116.1 -2461.8 4923.6 model5_b4 24 4970.8 5132.7 -2461.4 4922.8 0.8177 2 0.6644 5. Analysis of the subset of successful learners Task 1 Emmeans: > pairs(emm6_b1, adjust = "bonferroni") trial = itemNonA: contrast estimate SE df z.ratio p.value A1 - NA1 0.49606 0.203 Inf 2.447 0.0432 A1 - Mix -0.08251 0.179 Inf -0.461 1.0000 NA1 - Mix -0.57857 0.205 Inf -2.817 0.0145 trial = itemA: contrast estimate SE df z.ratio p.value A1 - NA1 0.31351 0.237 Inf 1.322 0.5588 A1 - Mix 0.33733 0.209 Inf 1.616 0.3181 NA1 - Mix 0.02382 0.233 Inf 0.102 1.0000 trial = itemBL_A: contrast estimate SE df z.ratio p.value A1 - NA1 0.20357 0.247 Inf 0.823 1.0000 A1 - Mix -0.03067 0.226 Inf -0.136 1.0000 NA1 - Mix -0.23424 0.251 Inf -0.933 1.0000 trial = itemBL_NA: contrast estimate SE df z.ratio p.value A1 - NA1 0.35611 0.285 Inf 1.249 0.6346 A1 - Mix 0.34814 0.261 Inf 1.332 0.5481 NA1 - Mix -0.00797 0.277 Inf -0.029 1.0000 Results are averaged over the levels of: familiarity Results are given on the log odds ratio (not the response) scale. P value adjustment: bonferroni method for 3 tests Task2 Emmeans > pairs(emm6_b2, adjust = "bonferroni") trial = itemA: contrast estimate SE df z.ratio p.value A1 - NA1 1.170 0.936 Inf 1.249 0.6345 A1 - Mix 1.572 0.824 Inf 1.908 0.1691 127 NA1 - Mix 0.402 0.728 Inf 0.552 1.0000 trial = itemBL_A: contrast estimate SE df z.ratio p.value A1 - NA1 -0.674 0.916 Inf -0.736 1.0000 A1 - Mix -0.246 0.763 Inf -0.322 1.0000 NA1 - Mix 0.428 0.811 Inf 0.529 1.0000 Results are averaged over the levels of: familiarity Results are given on the log odds ratio (not the response) scale. P value adjustment: bonferroni method for 3 tests Task3 Emmeans > pairs(emm4_b3, adjust = "bonferroni") trial = itemNonA: contrast estimate SE df z.ratio p.value A1 - NA1 -1.977 1.496 Inf -1.322 0.5583 A1 - Mix -1.547 1.300 Inf -1.191 0.7014 NA1 - Mix 0.430 1.341 Inf 0.321 1.0000 trial = itemA: contrast estimate SE df z.ratio p.value A1 - NA1 1.664 1.448 Inf 1.149 0.7511 A1 - Mix 1.361 1.367 Inf 0.995 0.9591 NA1 - Mix -0.304 0.976 Inf -0.311 1.0000 trial = itemBL_A: contrast estimate SE df z.ratio p.value A1 - NA1 -0.537 0.961 Inf -0.559 1.0000 A1 - Mix -1.207 0.933 Inf -1.294 0.5874 NA1 - Mix -0.670 0.820 Inf -0.817 1.0000 trial = itemBL_NA: contrast estimate SE df z.ratio p.value A1 - NA1 0.414 0.849 Inf 0.487 1.0000 A1 - Mix 0.149 0.785 Inf 0.189 1.0000 NA1 - Mix -0.265 0.593 Inf -0.448 1.0000 Results are given on the log odds ratio (not the response) scale. P value adjustment: bonferroni method for 3 tests 6. Analysis of the segmentation accuracy Logistic regression model: Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) [glmerMod] Family: binomial ( logit ) Formula: responses ~ conditions + trials + acc + (1 + trials | subject) + 128 (1 + conditions | stimulus) Data: data_s1 Control: glmerControl(optimizer = "optimx", calc.derivs = FALSE, optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE)) AIC BIC logLik deviance df.resid 5775.2 5930.4 -2864.6 5729.2 6274 Scaled residuals: Min 1Q Median 3Q Max -6.9966 0.1751 0.3267 0.5181 1.9099 Random effects: Groups Name Variance Std.Dev. Corr subject (Intercept) 0.15000 0.3873 trialsitemA 0.34288 0.5856 -0.45 trialsitemBL_A 0.40546 0.6368 -0.26 0.89 trialsitemBL_NA 0.55866 0.7474 0.05 0.86 0.78 stimulus (Intercept) 0.96203 0.9808 conditionsNA1 0.09705 0.3115 -1.00 conditionsMix 0.02924 0.1710 -0.42 0.42 Number of obs: 6297, groups: subject, 198; stimulus, 32 Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) -0.26268 0.36796 -0.714 0.475293 conditionsNA1 -0.33948 0.12798 -2.653 0.007985 ** conditionsMix -0.01529 0.12426 -0.123 0.902038 trialsitemA 0.71396 0.36022 1.982 0.047475 * trialsitemBL_A 1.23056 0.36911 3.334 0.000856 *** trialsitemBL_NA 1.32407 0.37787 3.504 0.000458 *** acc 2.10837 0.37946 5.556 2.76e-08 *** --- Logistic regression model 2 Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) [glmerMod] Family: binomial ( logit ) Formula: responses ~ conditions + trials + acc + conditions * acc + (1 + trials | subject) + (1 + conditions | stimulus) Data: data_s1 Control: glmerControl(optimizer = "optimx", calc.derivs = FALSE, optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE)) AIC BIC logLik deviance df.resid 5777.6 5946.3 -2863.8 5727.6 6272 Scaled residuals: 129 Min 1Q Median 3Q Max -6.9312 0.1750 0.3264 0.5177 1.9665 Random effects: Groups Name Variance Std.Dev. Corr subject (Intercept) 0.14147 0.3761 trialsitemA 0.34087 0.5838 -0.43 trialsitemBL_A 0.40245 0.6344 -0.26 0.89 trialsitemBL_NA 0.56340 0.7506 0.07 0.87 0.78 stimulus (Intercept) 0.96835 0.9840 conditionsNA1 0.09998 0.3162 -1.00 conditionsMix 0.02967 0.1723 -0.44 0.44 Number of obs: 6297, groups: subject, 198; stimulus, 32 Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) -0.6725 0.4964 -1.355 0.175486 conditionsNA1 0.3385 0.5525 0.613 0.540177 conditionsMix 0.4919 0.5733 0.858 0.390861 trialsitemA 0.7132 0.3588 1.988 0.046819 * trialsitemBL_A 1.2297 0.3677 3.344 0.000825 *** trialsitemBL_NA 1.3280 0.3769 3.524 0.000426 *** acc 2.8380 0.7062 4.019 5.84e-05 *** conditionsNA1:acc -1.1952 0.9453 -1.264 0.206123 conditionsMix:acc -0.8875 0.9523 -0.932 0.351346 Logistic regression model 3 Generalized linear mixed model fit by maximum likelihood (Laplace Approximation) [glmerMod] Family: binomial ( logit ) Formula: responses ~ conditions + trials + acc + trials * acc + (1 + trials | subject) + (1 + conditions | stimulus) Data: data_s1 Control: glmerControl(optimizer = "optimx", calc.derivs = FALSE, optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE)) AIC BIC logLik deviance df.resid 5777.0 5952.4 -2862.5 5725.0 6271 Scaled residuals: Min 1Q Median 3Q Max -7.3655 0.1712 0.3245 0.5219 1.9387 Random effects: Groups Name Variance Std.Dev. Corr subject (Intercept) 0.13318 0.3649 trialsitemA 0.30791 0.5549 -0.38 trialsitemBL_A 0.38594 0.6212 -0.18 0.87 130 trialsitemBL_NA 0.53793 0.7334 0.13 0.86 0.76 stimulus (Intercept) 0.95614 0.9778 conditionsNA1 0.09517 0.3085 -1.00 conditionsMix 0.03293 0.1815 -0.35 0.35 Number of obs: 6297, groups: subject, 198; stimulus, 32 Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) 0.15567 0.41776 0.373 0.70942 conditionsNA1 -0.33908 0.12773 -2.655 0.00794 ** conditionsMix -0.01339 0.12495 -0.107 0.91464 trialsitemA -0.05066 0.57922 -0.087 0.93030 trialsitemBL_A 0.37156 0.61750 0.602 0.54737 trialsitemBL_NA 0.52164 0.65476 0.797 0.42563 acc 1.37824 0.50783 2.714 0.00665 ** trialsitemA:acc 1.33260 0.78463 1.698 0.08944 . trialsitemBL_A:acc 1.49199 0.85787 1.739 0.08200 . trialsitemBL_NA:acc 1.39314 0.92746 1.502 0.13307 --- 2 main effects (without acc score) vs 3 main effects Models: model1_b1: responses ~ conditions + trials + (1 + trials | subject) + (1 + conditions | stimulus) model9_b1: responses ~ conditions + trials + acc + (1 + trials | subject) + (1 + conditions | stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model1_b1 22 5799.4 5947.9 -2877.7 5755.4 model9_b1 23 5775.2 5930.4 -2864.6 5729.2 26.178 1 3.113e-07 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 3 main effects (without interaction) vs with interaction of accuracy score and trials Models: model9_b1: responses ~ conditions + trials + acc + (1 + trials | subject) + (1 + conditions | stimulus) model8_b1: responses ~ conditions + trials + acc + trials * acc + (1 + trials | subject) + (1 + conditions | stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model9_b1 23 5775.2 5930.4 -2864.6 5729.2 model8_b1 26 5777.0 5952.4 -2862.5 5725.0 4.2351 3 0.2372 3 main effects (without interaction) vs with interaction of accuracy score and condition Models: model9_b1: responses ~ conditions + trials + acc + (1 + trials | subject) + (1 + conditions | stimulus) 131 model10_b1: responses ~ conditions + trials + acc + conditions * acc + (1 + trials | subject) + (1 + conditions | stimulus) npar AIC BIC logLik deviance Chisq Df Pr(>Chisq) model9_b1 23 5775.2 5930.4 -2864.6 5729.2 model10_b1 25 5777.6 5946.3 -2863.8 5727.6 1.6376 2 0.441
Thesis/Dissertation
eng
Linguistics
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Tessier, Anne-Michelle, 1979-
Learning morpho-phonological alternations like French liaison : an artificial language learning study
Text