West Coast Conference on Formal Linguistics (WCCFL) (38th : 2020)

Avoiding multiple reduplication without INTEGRITY Mellesmoen, Gloria; Urbanczyk, Suzanne 2020-03-06

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West Coast Conference in Formal Linguistics 38 - March 6, 2020    Mellesmoen & Urbanczyk 1   Avoiding multiple reduplication without INTEGRITY1 Gloria Mellesmoen, University of British Columbia Suzanne Urbanczyk, University of Victoria  1 Introduction  1.1 The Typology of Multiple Reduplication   Multiple reduplication (MR) is marked cross-linguistically, but relatively common across the Salish language family.2  Comox-Sliammon: C1 ‘imperfective’ and C2 ‘inchoative’  (1) qə~qx~̣əx ̣IPFV~more~INCH ‘getting to be more’     (Fieldwork Notes – August 4, 2018)  Lushootseed: C1C2- ‘plural’ and C2 ‘out of control’   (2) sáxʷ~axʷ~saxʷ-əb PL~OOC~jump-MD ‘many scurrying all around’    (Hess 1967; Bates, Hess & Hilbert 1994)  Lillooet: -C1- ‘diminutive’ and C1C2- ‘plural’  (3) n-zəw~zəw~ə́w̓-ks-tən LOC-PL~scoop.liquid~DIM-hand-INST ‘little cups’      (van Eijk 1981)3  ★  Zimmermann (to appear) proposes the following cross-linguistic MR patterns:   ○ Faithful: MR is tolerated and surfaces as expected  ○ Subtracting: MR is allowed only with restrictions on reduplicant size  ○ Avoidance: MR is completely absent    ★ In this paper, we expand the typology and describe a fourth approach to MR attested in Hul’q’umi’num’ (Central Salish):  ○ Variable MR: MR occurs, but is blocked if other (non-reduplicative) allomorphs can be recruited to express the same meaning.   1 We would like to thank Tom Hukari for sharing an electronic dictionary of Hul’q’umi’num’ with us. Also thanks to Donna Gerdts and Ruby Peter for sharing so much of their knowledge about Hul’q’umi’num’. 2 Unless otherwise noted, all data are represented in the North American Phonetic Alphabet (NAPA). Abbreviations used include: CTR ‘control transitive’, DIM ‘diminutive’, INCH ‘inchoative’, INST ‘instrumental’, IPFV ‘imperfective’, LOC ‘locative’, OCC ‘out-of-control’, PL ‘plural’, and MD ‘middle.  3 Thank you to Henry Davis for providing the gloss for this form. West Coast Conference in Formal Linguistics 38 - March 6, 2020    Mellesmoen & Urbanczyk 2  ★ Variable MR raises theoretical challenges for the analysis of reduplication.   ○ It is not enough to appeal to constraints on reduplicant size or shape.  ○ Variable MR in Hul’q’umi’num’ requires restrictions on copying in GEN.  1.2 Overview of Variable MR in Hul’q’umi’num’ (Central Salish) and Theoretical Questions  ★ Fact #1: Reduplication is used to mark imperfective, plural, and diminutive on verbs.4  (4) a. ɬá~ɬək̓ʷ IPFV~fly ‘flying’       (Hukari 1978:163)  b. θəx~̣θə́x-̣ət  PL-push-CTR ‘pushing them’     (Hukari 1978:189)  c. k̓ʷiʔ-k̓ʷéɬ-t    DIM~pour-CTR  ‘pouring it (dim.)’     (Hukari 1978:194)  ★ Fact #2: Multiple reduplication is attested in the language.  (5) a. ɬə~ɬá<ʔ>~ɬək̓ʷ  DIM~IPFV<DIM>~fly ‘flying (dim.)’      (Hukari 1978:196)  b. t̓ə~t̓í<ʔ>~t̓əl-əm DIM~IPFV~<DIM>~sing-MD ‘singing (dim.)’      (Hukari 1978:196)  ★ Fact #3: Imperfective, plural, and diminutive co-occur, but multiple reduplication is more restricted.    (6) pəliʔpáqʷt  p<əl>i<ʔ>~p<á>qʷ-t     DIM<PL><DIM>~break<IPFV>-CTR   ‘breaking (dim. pl.)’      (Hukari 1978:196)  The challenge: The plural -l- infix occurs, rather than reduplication (*piʔpəqʷpáqʷt), despite reduplication being the preferred allomorph in the verbal domain (Hukari 1978).   Our solution: MR is banned by a binarity restriction on GEN: one input segment can maximally correspond to two output segments.5     4 We set aside nominal reduplication here, as well as a C1 “resultative” reduplication pattern. Other (non-reduplicative) allomorphs for the three types of reduplication considered are given in the following sections.  5 MR may arise, as in (6), but this where reduplication has occurred in different strata. West Coast Conference in Formal Linguistics 38 - March 6, 2020    Mellesmoen & Urbanczyk 3  2 Analysis of Variable MR in Hul’q’umi’num’  2.1 Hul’q’umi’num’ Data  ★ We focus on the three types of reduplication in Hul’q’umi’num’ that co-occur on verbs:  ○ C1- Imperfective (IPFV)  ○ C1C2- Plural (PL)  ○ C1- Diminutive (DIM)   ★ While each of these functions may be associated with reduplication in isolation, the imperfective and plural also have non-reduplicative allomorphs.  ★ Data are from Hukari (1978) and Hukari & Peter (1995).   2.2 Main Theoretical Assumptions  ★ We adopt a Stratal OT approach, focusing on a stem-level and a word-level (Kiparsky 2007, 2014; Bermúdez-Otero, 2012).  ○ The input to the stem-level is a set of morphemes (from the lexicon).  ○ The input to the word-level is the output of the stem-level.    3 Stem-Level Reduplication: Imperfective  ★ Imperfective aspect is expressed by the largest range of non-concatenative allomorphs and may be realized with: reduplication (7a), ablaut (7b), metathesis (7c), a glottal stop infix (7d), sonorant debuccalization (7e), among other stem modification, all of which are accompanied by resonant glottalization.   (7) a.  ɬíc̓ət  ‘cut it’   ɬí-ɬəc̓ət  ‘cutting it’ b. ɬə́p̓t̓ᶿt  ‘slurp it’  ɬép̓t̓ᶿt  ‘slurping it’ c. pqʷát  ‘break it (substance)’ páqᵂt  ‘breaking it’ d. hésəm  ‘sneeze’  héʔsəm̓ ‘sneezing’  e. lə́c̓ət  ‘fill it’   hə́l̓c̓t  ‘filling it’  Assumptions:  ★ Following Urbanczyk’s (1998) analysis of the ‘continuative’ in Upriver Halkomelem and others on the cognate ‘actual’ morpheme in Straits (Stonham, 1990; Bye & Svenonius, 2012), we assume the IPFV is a mora /µ/ (c.f. Zimmermann, 2013, 2017 on the cognate pattern in Stó:lo Halq’emeylem).   ★ We also assume that IPFV is attached first, at the stem-level (see Hukari, 1978 for a similar assumption regarding which non-concatenative morpheme is attached first).    West Coast Conference in Formal Linguistics 38 - March 6, 2020    Mellesmoen & Urbanczyk 4  (8) Stem-level vowel alternation & imperfective  a. lémət  ‘look at s.t.’  lél̓əm̓ət ‘looking at s.t.’ b. láməθət  ‘look at self’  lál̓əm̓əθət ‘looking at self’  ★ Reduplication is accomplished via fission of an input segment into two output segments, in order to fill an empty prosodic unit (Bye & Svenonius 2012; Saba Kirchner 2013; Urbanczyk 1998; Zimmermann 2013 and others). This violates INTEGRITY:  (9) INTEGRITY   No element of the input has multiple correspondents in the output.  ★ A glottal stop is inserted to fill the mora, violating DEP-C.  (10) DEP-C     Every consonant in the output has a correspondent in the input.   ★ Schwa is not moraic (Shaw et al. 1999), but codas are.    ★ Constraints on well-formedness determine the correct allomorph.  ★ Reduplication is compelled in order to satisfy *FLOAT, which bans unaffiliated prosodic units (Saba Kirchner, 2013: 232)  (11) *FLOAT ∀p ∈ O, where p is a prosodic unit: ∃s, where s is a segment, and p dominates s.  (12)  /µ- ɫic̓-ət/ *FLOAT DEP-C INTEGRITY   a.  µ ɫíc̓ət *!    ☞ b.  ɫíɫəc̓ət   *   c.  ɫíʔc̓ət  *!   ★ Reduplication is preferred over glottal stop insertion, indicating that DEP-C >> INTEGRITY.  ★ Strengthening of schwa to a full vowel fills the mora in the ablaut cases.  ★ In order to rule out candidate (14.c) with glottal stop insertion, a constraint against schwa-glottal stop in coda position must be active in the language (see Bessell & Czaykowska-Higgins, 1993).   (13) *əʔ]σ Schwa is not permitted before a glottal stop that is in a coda.          West Coast Conference in Formal Linguistics 38 - March 6, 2020    Mellesmoen & Urbanczyk 5   (14)   /µ-ɫəpt̓ᶿ-t/ *FLOAT *əʔ]σ DEP-C IDENT-V INTEGRITY     a.  µ ɫə́pt̓ᶿt *!       ☞ b. ɫépt̓ᶿt    *      c. ɫə́ʔpt̓ᶿt  *! *       d. µ ɫə́ɫəpt̓ᶿ *!    *  ★ Because schwa is not moraic, reduplication will not fill the mora, ruling out candidate d.   ★ Metathesis pattern is epiphenomenal: the ablaut vowel occurs in the root, not the affix.    (15)   /µ- pqʷ-t/ *FLOAT *əʔ]σ DEP-C IDENT-V INTEGRITY     a.  µ pqʷát *!       ☞ b. páqʷt            c.  pəʔqʷt  *! *       d. µ pə́pqʷt *!    *  ★ Intervocalic /h/ is rare in Hul’q’umi’num’:  ○ It only occurs before schwa in the context when the sonorant changes to schwa and multiple reduplication is observed (see below).  ○ Search of the Hul’q’umi’num’ Dictionary: [Vhə] does not occur otherwise.   (16) *Vhə Schwa is not permitted after /h/  (17)   /µ- hes-əm/ *FLOAT *Vhə *əʔ]σ DEP-C IDENT-V INTEGRITY     a.  µ hésəm *!        ☞ b. héʔsəm     *       c. héhəsəm  *!    *  West Coast Conference in Formal Linguistics 38 - March 6, 2020    Mellesmoen & Urbanczyk 6  ★ Hukari (1977) provides evidence that /h/ arises in some reduplicative contexts as the result of sonorant aspiration, rather than epenthesis, hence the constraint *RiəRi.   (18) *RiəRi  Schwa is not permitted between a series of identical sonorants   ★ There is no evidence that [h] is epenthetic.   ○ See also Gerdts & Werle (2014): the epenthetic consonant is /ʔ/, rather than /h/.  ★ The sonorant is in the coda and is moraic.   ★ The ‘imperfective’ has one mora more:   (19)   /µ-lə́c̓-ət/ *FLOAT *Vhə *əʔ]σ *RiəRi DEP-C IDENT-V INTEG IDENT-SON     a.  µ lə́c̓ət *!          ☞ b. hə́l̓c̓ət        * *    c. µ lələ́c̓ət *!   *       *      d. lə́l̓c̓ət    *!       *      e. léc̓ət      *!       f. lə́ʔc̓ət   *!  *     ★ Summary: IPFV allomorphy can be analyzed by addition of a /µ/ at the stem level   4 Word-Level Reduplication (Diminutive and Plural)  4.1 Diminutive Reduplication  ★ The diminutive is marked with a reduplicative morpheme (C1ə- or C1i-), and is accompanied by a glottal stop infix.  ★ Observe the placement of the glottal infix: it is internal to the stem (beside the stressed vowel) when the root has a full vowel (20), but between reduplicant and stem (beside the epenthetic /i/) otherwise (21).  ★ Diminutive verbs are always in the imperfective aspect in Hul’q’umi’num’ (DIM).    West Coast Conference in Formal Linguistics 38 - March 6, 2020    Mellesmoen & Urbanczyk 7     ★ The combination of the diminutive and imperfective may result in MR (20).  (20)  IPFV     DIM-IPFV  a. ɫáɫək̓ʷ  ‘flying’  ɫəɫáʔɫək̓ʷ ‘flying (dim.)’ b. ɫéɫəqəm̓ ‘whispering’  ɫəɫéʔɫəqəm̓ ‘whispering (dim.)’  (21)  IPFV     DIM-IPFV    a. k̓ʷéɫt  ‘pouring it’  k̓ʷiʔk̓ʷéɫt ‘pouring it (dim.)’ b. ƛ̓épxṭ  ‘sprinkling it’  ƛ̓iʔƛ̓épxṭ ‘sprinkling it (dim.)’ c. hə́l̓c̓t  ‘filing’   hiʔhə́l̓c̓t `filling (dim.)’   Assumptions:  ★ Diminutive occurs at the word-level, the input to the word-level already includes the imperfective morpheme (from the stem-level).   ★ We assume that the diminutive morpheme involves the affixation of a syllable and a glottal stop, which may surface in a position that is discontinuous from copied material.  ○ We only include candidates with /ʔ/ in the correct position, for ease of exposition.  ○ The default (non-schwa) vowel is /i/.   ★ MAX, like *FLOAT, must be highly ranked because both parts of the diminutive (reduplication and glottal stop) always surface.   ★ The constraint *əʔ]σ motivates the insertion of the full (moraic) vowel, rather than schwa. (compare 26b and 26e.)  ★ INTEGRITY is split into two constraints: INTEGRITY-V and INTEGRITY-C.  (22) INTEGRITY-V: No input vowel has multiple correspondents in the output  (23) INTEGRITY-C: No input consonant has multiple correspondents in the output  ★ INTEGRITY-V (INT-V) must be ranked above DEP and INTEGRITY-C (INT-C) to motivate vowel epenthesis, rather than copying a vowel.6 (Compare 25b and 25c.)  ★ A constraint against having unstressed full vowels is needed to rule out [i] in (25a).   (24) *V̆: Do not have an unstressed full vowel      6 This is consistent with Hukari’s (1978: 195) observation: “it turns out that the imperfective and resultative stem vowels are never copied with the diminutive […]”. West Coast Conference in Formal Linguistics 38 - March 6, 2020    Mellesmoen & Urbanczyk 8   (25)   DIM{σ+ʔ} + ɫáɫək̓ʷ *FLOAT MAX *əʔ]σ INT-V *V̆ DEP INT-C     a. ɬiɬáʔɬək̓ʷ     *! * *   ☞ b. ɬəɬáʔɬək̓ʷ      * *   c. ɬaɬáʔɬək̓ʷ    *! *  *  (26)   DIM{σ+ʔ} + k̓ʷéɬt *FLOAT MAX *əʔ]σ INT-V *V̆ DEP INT-C     a. k̓ʷik̓ʷéɬt  *!   * * *   ☞ b. k̓ʷiʔk̓ʷéɬt     * * *     c. k̓ʷeʔk̓ʷéɬt    *! *  *     d. σ k̓ʷéɬt *! *          e. k̓ʷəʔk̓ʷéɬt   *!   * *  ★ Summary: Reduplication fills the empty syllable, and /i/ is compelled by *əʔ]σ  in (26b)   4.2 Plural Reduplication  ★ Verbal plurality can be marked by C1əC2- reduplication (27a) or an infixed -l- (with schwa epenthesis) (27b).   (27) a. t̓íləm  ‘to sing’  t̓əlt̓íləm ‘they sing’    lémət  ‘to look at s.t.’  ləmlémət ‘to look at them’    ʔíməš  ‘walk’   ʔəmʔíməš ‘walking around’    mə́q̓ət  ‘to swallow s.t.’ məq̓mə́q̓ət ‘swallowing PL’    sə́t̓q̓t  ‘disturb’  sət̓sə́t̓q̓t ‘disturb (repeatedly)’    k̓ʷɬét  ‘pour it (liquid)’ k̓ʷəɬk̓ʷə́ɬt ‘pour out things’  b. ném̓  ‘go’   néləm̓  ‘they go’    k̓ʷés  ‘hot (get hot)’  k̓ʷél̓əs  ‘hot, warm weather’   técəl  ‘arrive, reach’  tél̓əcəl  ‘arrive PL’  Assumptions:   ★ The plural is a word-level process (evaluated under the same ranking as the diminutive).  ★ There are two distinct (listed) allomorphs of the plural: an -l- infix and reduplication.   ○ The plural reduplicative allomorph consists of a syllable with one mora.  West Coast Conference in Formal Linguistics 38 - March 6, 2020    Mellesmoen & Urbanczyk 9  ○ We treat C1C2 reduplication as the default realization of the plural and analyse the choice of allomorph with preferential allomorph selection (Mascaró, 2007).   ○ In this approach, a candidate that selects the lower ranked allomorph (-l-) incurs a violation under PRIORITY, meaning PRIORITY >> INTEGRITY-C  (28)   PL{σµ1, -l-2} + t̓íləm PRIORITY INTEGRITY-C   ☞ a. t̓əlt̓íləm         **     b. t̓íl2ələm         *!   ★ The high ranking of *FLOAT means that both the syllable (and its associated mora) must be associated with segmental content in the output. (See 29b and 29d.)  ★ The ranking of INT-V >> INT-C (established in the discussion of the diminutive) correctly predicts reduplication of C2 (see a), rather than the vowel (see c), each of which would be a light syllable.  (29)   PL{σμ1, -l-2} +  t̓íləm  *FLOAT MAX *əʔ]σ INT-V PRIORITY *V̆ DEP INT-C CONTIG   ☞ a. t̓əlt̓íləm       * **      b. μ t̓ət̓íləm *!      * *      c. t̓it̓íləm    *!  *  *      d. σμ t̓íləm *!             e. t̓íl2ələm     *!  *  *  (30)   PL{σμ1, -l-2} + mə́q̓ət  *FLOAT MAX *əʔ]σ INT-V PRIORITY *V̆ DEP INT-C CONTIG   ☞ a. məq̓mə́q̓ət       * **      b. µ məmə́q̓ət *!      * *      c. mimə́q̓ət      *! * *      d. mə́l2əq̓ət     *!  *  *     e. σμ  mə́q̓ət *!             f. məq̓ət2  *!   *      West Coast Conference in Formal Linguistics 38 - March 6, 2020    Mellesmoen & Urbanczyk 10  ★ Summary: The optimal candidate has a reduplicant exponent, compelling violation of INTEG-C twice, in order to fill a mora/syllable.    4.2.1 Imperfective and Plural  ★ When IPFV and PL occur together (shaded cells), only one copy occurs, even when MR would be predicted on the basis of their forms in isolation as in (31a).   ★ Compare the imperfective singular form and the plural perfective forms, which each have a different reduplicant: we find t̓íl̓t̓ə́ləm̓ rather than *t̓əl̓t̓ít̓ə́ləm̓.   (31)  PFV     IPFV   a. SG t̓íləm  ‘to sing’ t̓ít̓ələm̓  ‘singing’    PL t̓əlt̓íləm ‘they sing’ t̓íl̓t̓ə́ləm̓ ‘they are singing’  b. SG pqʷát  ‘break it’ páqʷt  ‘breaking it’ PL pəqʷpə́qʷət ‘break them’ pəqʷpáqʷt ‘breaking them’  ★ The constraint rankings established so far will choose the optimal candidate without  multiple reduplication when plural and imperfective morphemes co-occur.   (32)  PL{σμ1, -l-2} +  t̓ít̓ələm̓  *FLOAT MAX *əʔ]σ INT-V PRIORITY *V̆ DEP INT-C CONTIG   ☞ a. t̓ílt̓ələm̓        * *     b. μ t̓ít̓ələm̓ *!             c. t̓ət̓t̓ít̓ələm̓       *! **      d. t̓əlt̓ít̓ələm̓       *! **      e. t̓íl2ət̓ələm̓     *!  *  *     f. t̓əl̓t̓ít̓ə́ləm̓        *!  **    ★ Notice that the ‘coalescence’ of PL-IPFV follows from the constraint rankings established thus far. Nothing new needs to be added to the analysis to achieve this result.  ★ We now analyse double reduplication with the resonant-initial, schwa-vowelled roots.    West Coast Conference in Formal Linguistics 38 - March 6, 2020    Mellesmoen & Urbanczyk 11  (33)  PL{σμ1, -l-2} + hə́m̓q̓ət *FLOAT MAX *əʔ]σ INT-V PRIORITY *V̆ DEP INT-C CONTIG   ☞ a. həm̓hə́m̓q̓ət       * **      b. µ həhə́m̓q̓ət *!      * *      c. hihə́m̓q̓ət      *! * *      d. hə́l2əm̓q̓ət     *!  *  *     e. σµ hə́m̓q̓ət *!          (34)   PL{σμ1,-l-2} + θéxṭ *FLOAT MAX *əʔ]σ INT-V PRIORITY *V̆ DEP INT-C CONTIG   ☞ a. θəxθ̣éxṭ       * **      b. θeθéxṭ    *!  *  *      c. µ θəθéxṭ *!      * *      d. σµ θéxṭ *!             e. θél2əxṭ     *!  *  *   4.2.2 Imperfective Diminutive Plural  ★ When all three of the morphemes (diminutive, plural, and imperfective) co-occur, MR is not found. The plural -l- infix is selected, rather than the predicted C1əC2- reduplicant (*piʔpəqʷpaqʷt).  (35)  DIM-IPFV    DIM-IPFV-PL a. t̓ət̓íʔt̓ələm̓ singing (DIM)  t̓əlíʔt̓ələm̓ singing (DIM) b. piʔpaqʷt breaking it (DIM) pəliʔpaqʷt breaking them (DIM)  ★ Given the analytic assumptions made regarding allomorph selection, the expected form is predicted to involve MR.   ○ This is possible if GEN can create candidate forms that have more than two output correspondents for one input segment.   West Coast Conference in Formal Linguistics 38 - March 6, 2020    Mellesmoen & Urbanczyk 12  (36)   PL{σμ1, -l-2} + DIM{σ+ʔ} +  paqʷt *FLOAT MAX *əʔ]σ INT-V PRIORITY *V̆ DEP INT-C CONTIG     a. pəl2iʔpáqʷt     *! * ** *      b. σµ piʔpáqʷt *!     * * *    L c. piʔpəqʷpáqʷt      * ** ***    d. pəl2aʔpáqʷt    *!  * * *   ★ But, with the proposed constraint on GEN… *piʔpəqʷpaqʷt is not possible candidate!!  (37) GEN correspondence restriction: an element in the input can correspond to a maximum of two output elements  ★ Figure 1. illustrates how MR is achieved (1st column) as well as the candidate that would not be produced by GEN, given our proposal (2nd column), and the candidate that is produced by GEN in which Variable MR occurs (3rd column).       Figure 1.   Word-Level:  (38)   PL{σμ1, -l-2} + DIM{σ+ʔ} +  paqʷt *FLOAT MAX *əʔ]σ INT-V PRIORITY *V̆ DEP INT-C CONTIG   ☞ a. pəliʔpáqʷt     * * ** *      b. σµ piʔpáqʷt *!     * * *   ★ PRIORITY is violated in order to realize a non-reduplicated morpheme, to satisfy *FLOAT.  West Coast Conference in Formal Linguistics 38 - March 6, 2020    Mellesmoen & Urbanczyk 13   5 Discussion & Implications  ★ By restricting how copying occurs – only allowing ONE fission of a segment – MR is predicted to be impossible within the same stratum.   ○ This prediction is borne out by examining cases of MR, such as found in Interior Salish languages (Broselow, 1983), the Central Salish language Lushootseed (Broselow 1983; Urbanczyk 2006; Zimmermann to appear), Nuuchahnulth (Wakashan, Stonham, 2007), and Fox (Algonquian; Zimmermann to appear).  ○ In each of these languages, there is evidence that the second copy occurs in a separate stratum.  ★ Zimmermann’s (to appear) approach to avoidance of MR is to have coalescence of prosodic units; coalescence of prosodic units does not predict the selection of a non-reduplicative allomorph.   Q: What predictions do other approaches to reduplication make:    1) Base-Reduplicant Correspondence Theory (McCarthy & Prince, 1999) – each reduplicative morpheme is represented by RED, so unlimited number of reduplications are predicted.   2) Harmonic Template Satisfaction (McCarthy, Kimper, & Mullin, 2012)– each reduplicative morpheme is represented by an empty prosodic unit in the input. COPY  functions can occur for each prosodic unit, so unlimited number of reduplications predicted.  3) Morphological Doubling Theory (Inkelas & Zoll, 2006)– each reduplicative morpheme is represented as a Stem, analogous to compounding. Predicts that languages with compounds of more than three, will have more than two reduplications.  4) Generalized Non-Linear Affixation/Minimal Reduplication (Bermudez-Otero, 2012; Saba Kirchner, 2013; Zimmermann 2017) - each reduplicative morpheme is represented by a prosodic unit, with its phonological content determined by violating INTEGRITY. There is nothing to constrain a 1:3 or 1:4 correspondent relation, so triple or quadruple reduplication in one stratum is predicted.  ★ A further prediction: MR is possible in the same stratum, but only if the reduplicative morphemes target different parts of the word, so that each RED copies different segments of the word.   Selected References  Bermúdez-Otero. R. (2012). The architecture of the grammar and division of labor in exponence. In J. Trommer (ed). The morphology and phonology of exponence. Oxford, UK: Oxford University Press.  West Coast Conference in Formal Linguistics 38 - March 6, 2020    Mellesmoen & Urbanczyk 14  Broselow, E. (1983). Salish double reduplications: subjacency in morphology. Natural Language and Linguistic Theory 1: 317-346. Bye, P. and P. Svenonius. (2012). Non-concatenative morphology as epiphenomenon. In J. Trommer (ed). The morphology and phonology of exponence. Oxford, UK: Oxford University Press. Gerdts, D. & A. Werle. (2014). Halkomelem clitic types. Morphology 24: 245-281. Hess, T. M.  (1967). Snohomish grammatical structure (Unpublished doctoral dissertation). Hess, T., D. Bates, & V. Hilbert. (1994). Lushootseed Dictionary. Seattle, WA: University of Washington Press.  Hukari, T. (1977) Resonant devoicing in Cowichan. Canadian Journal of Linguistics 22: 47- 61. Hukari, T. (1978). Halkomelem nonsegmental morphology. Proceedings of ICSNL. Pp. 157-209. Hukari, T. & R. Peter. (1995). Cowichan dictionary. Duncan, BC: Cowichan Tribes.  Inkelas, S. & C. Zoll. 2006. Reduplication: Doubling in Morphology. Cambridge, UK: Cambridge University Press. Mascaró, J. (2007). External allomorphy and lexical representation. Linguistic Inquiry, 38(4), 715-735.  McCarthy, J., W. Kimper, & K. Mullin. (2012). Reduplication in Harmonic Serialism. Morphology 22: 173-232. McCarthy, J. & A. Prince. (1999). Faithfulness and Identity in Prosodic Morphology. In R. Kager, H. van der Hulst, & W. Zonneveld. The Prosody-Morphology Interface. Cambridge, UK: Cambridge University Press. Saba Kirchner, J. (2013). Minimal reduplication and reduplicative exponence. Morphology 23:227-243. Shaw, P., S.J. Blake, J. Campbell, & C. Sheperd. (1999). Stress in hən̓q̓əmin̓əm̓ (Musqueam) Salish. Workshop on the Structure and Constituency of the Languages of the Americas 4: 131-164. Stonham, J. (2007). Nuuchanulth double reduplication and Stratal Optimality Theory. Canadian Journal of Linguistics 52: 105 – 130.  Urbanczyk, S. (1998). Segment doubling and INTEGRITY violation.  West Coast Conference on Formal Linguistics 17, University of British Columbia. Vancouver, BC.  March. Urbanczyk, S. (2006). Reduplicative form and the root-affix asymmetry. Natural Language and Linguistic Theory 24, No.1: 179-240. van Eijk, J.  (1981).  Reduplication in lillooet.  In Papers  for  the  16th  international  conference  on  Salish  and  neighbouring  languages. Vancouver, BC: University of British Columbia Working Papers in Linguistics. Zimmermann, E. (2013).  Non-concatenative allomorphy is generalized prosodic affixation: The case of Upriver Halkomelem. Lingua 134: 1 – 26.  Zimmermann, E. (2017). Morphological length and defective morphemes. Oxford, UK: Oxford University Press.  Zimmermann, E. (to appear). Two is too much. . . in the phonology! A Phonological Account of Avoidance and Subtraction in Multiple Reduplication. The Linguistic Review.   


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