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Experimental Evidence for Quantum Structure in Cognition

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Quantum Interaction (QI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5494))

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Abstract

We prove a theorem that shows that a collection of experimental data of membership weights of items with respect to a pair of concepts and its conjunction cannot be modeled within a classical measure theoretic weight structure in case the experimental data contain the effect called overextension. Since the effect of overextension, analogue to the well-known guppy effect for concept combinations, is abundant in all experiments testing weights of items with respect to pairs of concepts and their conjunctions, our theorem constitutes a no-go theorem for classical measure structure for common data of membership weights of items with respect to concepts and their combinations. We put forward a simple geometric criterion that reveals the non classicality of the membership weight structure and use experimentally measured membership weights estimated by subjects in experiments from [26] to illustrate our geometrical criterion. The violation of the classical weight structure is similar to the violation of the well-known Bell inequalities studied in quantum mechanics, and hence suggests that the quantum formalism and hence the modeling by quantum membership weights, as for example in [17] , can accomplish what classical membership weights cannot do.

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Author information

Authors and Affiliations

  1. Leo Apostel Center, Brussels Free University, Brussels, Belgium

    Diederik Aerts & Sven Aerts

  2. Psychology and Computer Science, University of British Columbia, Canada

    Liane Gabora

Authors
  1. Diederik Aerts
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  2. Sven Aerts
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  3. Liane Gabora
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Editor information

Editors and Affiliations

  1. Faculty of Science and Technology, Queensland University of Technology, GPO Box 2434, 4001, Brisbane, Australia

    Peter Bruza

  2. Naval Research Laboratory, Navy Center for Applied Research in Artificial Intelligence, 4555 Overlook Avenue S.W, DC 20375, Washington, USA

    Donald Sofge

  3. Paine College, 1235 15th Street, P.O. Box, GA 30901-3182, Augusta, USA

    William Lawless

  4. Department of Computing Science, University of Glasgow, 17 Lilybank Gardens, G12 8QQ, Glasgow, UK

    Keith van Rijsbergen

  5. German Research Center for Artificial Intelligence, Stuhlsatzenhausweg 3, 66123, Saarbrücken, Germany

    Matthias Klusch

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Aerts, D., Aerts, S., Gabora, L. (2009). Experimental Evidence for Quantum Structure in Cognition. In: Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds) Quantum Interaction. QI 2009. Lecture Notes in Computer Science(), vol 5494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00834-4_7

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  • DOI: https://doi.org/10.1007/978-3-642-00834-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

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