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Editorial : Quantum Structures in Cognitive and Social Science Aerts, Diederik, 1953-; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro Apr 25, 2016

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EDITORIALpublished: 25 April 2016doi: 10.3389/fpsyg.2016.00577Frontiers in Psychology | www.frontiersin.org 1 April 2016 | Volume 7 | Article 577Edited and reviewed by:Bernhard Hommel,Leiden University, Netherlands*Correspondence:Sandro Sozzoss831@le.ac.ukSpecialty section:This article was submitted toCognition,a section of the journalFrontiers in PsychologyReceived: 05 April 2016Accepted: 07 April 2016Published: 25 April 2016Citation:Aerts D, Broekaert J, Gabora L andSozzo S (2016) Editorial: QuantumStructures in Cognitive and SocialScience. Front. Psychol. 7:577.doi: 10.3389/fpsyg.2016.00577Editorial: Quantum Structures inCognitive and Social ScienceDiederik Aerts 1, Jan Broekaert 1, Liane Gabora 2 and Sandro Sozzo 3*1Center Leo Apostel for Interdisciplinary Studies, Free University of Brussels, Brussels, Belgium, 2Department of Psychology,University of British Columbia, Kelowna, BC, Canada, 3 School of Management, Institute for Quantum Social and CognitiveScience, University of Leicester, Leicester, UKKeywords: quantum structures, quantum cognition, decision theory, human cognition, cognitive modelingThe Editorial on the Research TopicQuantum Structures in Cognitive and Social ScienceA fundamental problem in cognitive and social science concerns the identification of the principlesguiding human cognitive acts such as decision-making, categorization, and behavior underuncertainty. Identifying these mechanisms would have manifold implications for fields rangingfrom psychology to economics, finance, politics, computer science, and artificial intelligence. Thepredominant theoretical paradigm rests on a classical conception of logic and probability theory.According to this paradigm people make decisions by following the rules of Boole’s logic, whilethe probabilistic aspects of these decisions can be formalized by Kolmogorov’s probability theory.This classical approach was believed to provide a quite complete and accurate account of humandecision-making at both a normative level (describing what people should do) and a descriptivelevel (describing what people actually do). However, starting from the seventies, experimentalstudies of conceptual categorization, human judgment and perception, and behavioral economicshave revealed that this classical conception is fundamentally problematical, in the sense that thecognitive models based on these mathematical structures are not capable of capturing how humansmake decisions in situations involving uncertainty. In the last decade, an alternative scientificparadigm has arisen that employs a different and more general modeling scheme; it uses themathematical formalism of quantum theory to model situations and processes in cognitive andsocial science. This new approach has not only met with considerable success but is becomingincreasingly accepted in the scientific community, having attracted interest from importantscientists, top journals, funding institutions, and media. Prisoners’ dilemmas, conjunction anddisjunction fallacies, disjunction effects, violations of the Sure-Thing principle, Allais, Ellsbergand Machina paradoxes, are only some of the examples where the application of the quantummechanical formalism has shown significant effectiveness over traditional modeling schemes of aclassical type.The Frontiers Research Topic “Quantum Structures in Cognitive and Social Science” present anoverview of current research that applies the formalism of quantum theory to cognitive and socio-economic domains. The term “quantum” may be misleading. The aim here is not to investigatethe microphysical processes occurring in the human brain and, as a consequence, driving humanjudgments. Rather, we inquire into the validity of quantum theory as a general, coherent, andunitary paradigm for human cognition. In this respect, this research benefits from studies intothe axiomatic and operational foundations of quantum physics. The scope of this bold approachto human cognition is discovering general rules that associate the empirical phenomenology inthese domains with states, measurements, and probabilities of outcomes in such a way that theseentities are represented exactly as quantum theory inHilbert space represents states, measurements,and probabilities of outcomes in the phenomenology of microphysics. The ensuing modeling isAerts et al. Editorial: Quantum Structures in Cognitive and Social Sciencetheory-based, not experiment-based; that is, the models are notbuilt around a specific effect or experiment, although they aresometimes used in conjunction with empirical data to build astronger case. The models are constructed following the generalepistemological and technical constraints of quantum theory;hence the successes of this quantum theory-based modelingsuggest that it might provide a general theory for humancognition.This Research Topic develops around three main directions ofresearch, as follows.(i) The deep reasons underlying the success of the quantumparadigm in cognitive and socio-economic domains areinvestigated.(ii) Further empirical situations are identified in these domainswhere the quantum formalism presents advantages withrespect to traditional modeling schemes, and new genuinequantum structures appear.(iii) The application of this quantum paradigm is extended tonovel and barely explored domains.The first set of results concern knowledge representation andconceptual categorization. Aerts et al. analyze the results of acognitive test on conjunctions and negations of natural concepts,showing that a quantum-theoretic probabilistic model in Hilbertspace faithfully represents the collected data, at variance witha set-theoretic Kolmogorovian model. This result is explainedby assuming the existence of two types of reasoning in humancognition, a dominant emergent reasoning, and a secondarylogical reasoning. Some mathematical aspects of this quantum-theoretic model on conceptual conjunctions and negations aredeveloped in Veloz and Desjardins through the introduction ofunitary operators in Hilbert space. Aerts et al. show instead thatthe quantum-theoretic approach Aerts et al. can be interpretedas a suitable generalization of Rosch’s prototype theory, whereprototypes are context-dependent and may interfere whenconcepts combine.The second set of results concern the modeling of humandecision-making. Moreira and Wichert explore an alternativequantum-theoretic approach, the quantum-like Bayesiannetwork, to describe the paradoxes related to the violation of theSure-Thing Principle in experiments on human judgments. Theirmodel is in a good agreement with different sets of empiricaldata. The opinion paper in Pothos et al. reviews some currentprogress on the quantum similarity model in Hilbert spacerecently proposed by Pothos et al. which correctly representshuman similarity judgments. Decision-making errors andpreference reversal are also investigated in Yukalov and Sornettewithin their quantum decision theory. Wang and Busemeyeranalyze the notion of complementarity in human cognition, andclaim that the way in which it is used in quantum physics can alsobe helpful in cognitive science. Human perception is the object ofthe study in Khrennikov, where the author develops a quantummodel of the sensation-perception dynamics, illustrating itby means of the model of bistable perception of a specificambiguous figure, the Schröder stair. Finally, Tressoldi et al.identify a significant violation of temporal Bell inequalities ina set of cognitive tests. The violation indicates, according tothe authors, the presence of temporal entanglement betweenbinary human behavioral unconscious choices at a given timeand binary random outcomes at a different time. In all theseapproaches, the presence of quantum structures in cognitionis determined by the fact that the cognitive systems underinvestigation share a common feature, namely contextuality. Adifferent position with respect to the presence of contextuality incognition is assumed in Zhang and Dzhafarov, where the authorsapply a theory of (non)contextuality to analyze series-parallel(SP) mental architectures.The third set of results concern advanced applications ofthe quantum-mathematical formalism to wider ranges of socialscience. Bisconti et al. propose an inverse Potts model, typicallyused in statistical quantum field theory, to reconstruct thenode states in a real-world social network. Haven exploresthe properties of two types of potential functions, inspired byclassical and quantum physics that can be potentially employedto model financial information, including preferences towardrisk and uncertainty. Finally, Dalla Chiara et al. investigatedifferent, but mutually related, aspects of parallelism withinthe framework of quantum computation, cognition and music,and study potential applications of quantum computationalsemantics in both natural and musical language.Leaving aside the specific differences between the approachesabove, most of them agree in claiming that quantum structuresare systematically present in cognitive and social sciencephenomena, and that quantum-inspired models are moreefficient than traditional set-theoretic models of probability. Is“quantum” the end of the story? Is Hilbert space really theplace where all these phenomena can be modeled? Is there anyempirical deviation from quantum predictions? We do not haveyet an answer to these questions. This is why we believe thatthe road that will lead further to possibly a generally acceptedquantum theory of human decision-making will still be full offascinating surprises.AUTHOR CONTRIBUTIONSAll authors listed, have made substantial, direct, and intellectualcontribution to the work, and approved it for publication.Conflict of Interest Statement: The authors declare that the research wasconducted in the absence of any commercial or financial relationships that couldbe construed as a potential conflict of interest.Copyright © 2016 Aerts, Broekaert, Gabora and Sozzo. This is an open-access articledistributed under the terms of the Creative Commons Attribution License (CC BY).The use, distribution or reproduction in other forums is permitted, provided theoriginal author(s) or licensor are credited and that the original publication in thisjournal is cited, in accordance with accepted academic practice. No use, distributionor reproduction is permitted which does not comply with these terms.Frontiers in Psychology | www.frontiersin.org 2 April 2016 | Volume 7 | Article 577

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