Quantum Structure in Cognition: Why and How Concepts Are Entangled

  • Diederik Aerts
  • Sandro Sozzo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7052)

Abstract

One of us has recently elaborated a theory for modelling concepts that uses the state context property (SCoP) formalism, i.e. a generalization of the quantum formalism. This formalism incorporates context into the mathematical structure used to represent a concept, and thereby models how context influences the typicality of a single exemplar and the applicability of a single property of a concept, which provides a solution of the Pet-Fish problem and other difficulties occurring in concept theory. Then, a quantum model has been worked out which reproduces the membership weights of several exemplars of concepts and their combinations. We show in this paper that a further relevant effect appears in a natural way whenever two or more concepts combine, namely, entanglement. The presence of entanglement is explicitly revealed by considering a specific example with two concepts, constructing some Bell’s inequalities for this example, testing them in a real experiment with test subjects, and finally proving that Bell’s inequalities are violated in this case. We show that the intrinsic and unavoidable character of entanglement can be explained in terms of the weights of the exemplars of the combined concept with respect to the weights of the exemplars of the component concepts.

Keywords

Concept combination Bell’s inequalities entanglement quantum cognition 

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References

  1. 1.
    Hampton, J.A.: Overextension of Conjunctive Concepts: Evidence for a Unitary Model for Concept Typicality and Class Inclusion. J. Exp. Psych.: Lear. Mem. Cog. 14, 12–32 (1988)Google Scholar
  2. 2.
    Hampton, J.A.: Disjunction of Natural Concepts. Memory & Cognition 16, 579–591 (1988)CrossRefGoogle Scholar
  3. 3.
    Osherson, D.N., Smith, E.E.: On the Adequacy of Prototype Theory as a Theory of Concepts. Cognition 9, 35–58 (1981)CrossRefGoogle Scholar
  4. 4.
    Hampton, J.: Conceptual Combination. In: Lamberts, K., Shanks, D. (eds.) Knowledge, Concepts, and Categories, pp. 133–159. Psychology Press, Hove (1997)Google Scholar
  5. 5.
    Zadeh, L.: Fuzzy Sets. Information & Control 8, 338–353 (1965)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Zadeh, L.: A Note on Prototype Theory and Fuzzy Sets. Cognition 12, 291–297 (1982)CrossRefGoogle Scholar
  7. 7.
    Osherson, D.N., Smith, E.E.: Gradedness and Conceptual Combination. Cognition 12, 299–318 (1982)CrossRefGoogle Scholar
  8. 8.
    Komatsu, L.K.: Recent Views on Conceptual Structure. Psych. Bull. 112, 500–526 (1992)CrossRefGoogle Scholar
  9. 9.
    Fodor, J.: Concepts: A Potboiler. Cognition 50, 95–113 (1994)CrossRefGoogle Scholar
  10. 10.
    Rips, L.J.: The Current Status of Research on Concept Combination. Mind and Language 10, 72–104 (1995)CrossRefGoogle Scholar
  11. 11.
    Aerts, D.: A Possible explanation for the Probabilities of Quantum Mechanics. J. Math. Phys. 27, 202–210 (1986)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Aerts, D.: The Construction of Reality and Its Influence on the Understanding of Quantum Structures. Int. J. Theor. Phys. 31, 1815–1837 (1992)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Aerts, D.: Quantum Structures, Separated Physical Entities and Probability. Found. Phys. 24, 1227–1259 (1994)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Aerts, D.: Foundations of Quantum Physics: A General Realistic and Operational Approach. Int. J. Theor. Phys. 38, 289–358 (1999)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Gabora, L., Aerts, D.: Contextualizing Concepts Using a Mathematical Generalization of the Quantum Formalism. J. Exp. Theor. Art. Int. 14, 327–358 (2002)CrossRefMATHGoogle Scholar
  16. 16.
    Aerts, D., Gabora, L.: A Theory of Concepts and Their Combinations I: The Structure of the Sets of Contexts and Properties. Kybernetes 34, 167–191 (2005)CrossRefMATHGoogle Scholar
  17. 17.
    Aerts, D., Gabora, L.: A Theory of Concepts and Their Combinations II: A Hilbert Space Representation. Kybernetes 34, 192–221 (2005)CrossRefMATHGoogle Scholar
  18. 18.
    Aerts, D., Czachor, M., D’Hooghe, B.: Towards a Quantum Evolutionary Scheme: Violating Bell’s Inequalities in Language. In: Gontier, N., Van Bendegem, J.P., Aerts, D. (eds.) Evolutionary Epistemology, Language and Culture - A Non Adaptationist Systems Theoretical Approach, Springer, Dordrecht (2006)Google Scholar
  19. 19.
    Aerts, D.: Quantum Particles as Conceptual Entities. A Possible Explanatory Framework for Quantum Theory. Foundations of Science 14, 361–411 (2009)MATHGoogle Scholar
  20. 20.
    Aerts, D.: Quantum Structure in Cognition. J. Math. Psych. 53, 314–348 (2009)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Aerts, D., Aerts, S., Gabora, L.: Experimental Evidence for Quantum Structure in Cognition. In: Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds.) QI 2009. LNCS, vol. 5494, pp. 59–70. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  22. 22.
    Aerts, D., D’Hooghe, B.: Classical Logical Versus Quantum Conceptual Thought: Examples in Economy, Decision Theory and Concept Theory. In: Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds.) QI 2009. LNCS, vol. 5494, pp. 128–142. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  23. 23.
    Aerts, D., D’Hooghe, B., Haven, E.: Quantum Experimental Data in Psychology and Economics. Int. J. Theor. Phys. 49, 2971–2990 (2010)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Aerts, D.: Quantum Interference and Superposition in Cognition: Development of a Theory for the Disjunction of Concepts (2007), Archive reference and link: http://arxiv.org/abs/0705.1740
  25. 25.
    Aerts, D.: General Quantum Modeling of Combining Concepts: A Quantum Field Model in Fock Space (2007), Archive reference and link: http://arxiv.org/abs/0705.1740
  26. 26.
    Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed Experiment to Test Local Hidden-Variable Theories. Phys. Rev. Lett. 23, 880–884 (1969)CrossRefGoogle Scholar
  27. 27.
    Nelson, D.L., McEvoy, C.L.: Entangled Associative Structures and Context. In: Bruza, P.D., Lawless, W., van Rijsbergen, C.J., Sofge, D. (eds.) Proceedings of the AAAI Spring Symposium on Quantum Interaction. AAAI Press, Menlo Park (2007)Google Scholar
  28. 28.
    Bruza, P.D., Kitto, K., McEvoy, D., McEvoy, C.: Entangling Words and Meaning. In: Proceedings of the Second Quantum Interaction Symposium, pp. 118–124. Oxford University Press, Oxford (2008)Google Scholar
  29. 29.
    Bruza, P., Kitto, K., Nelson, D., McEvoy, C.: Extracting Spooky-Activation-at-a-Distance from Considerations of Entanglement. In: Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds.) QI 2009. LNCS, vol. 5494, pp. 71–83. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  30. 30.
    Aerts, D.: Interpreting Quantum Particles as Conceptual Entities. Int. J. Theor. Phys. 49, 2950–2970 (2010)MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Tsirelson, B.S.: Quantum Generalizations of Bell’s Inequality. Lett. Math. Phys. 4, 93 (1980)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Aerts, D., Czachor, M.: Quantum Aspects of Semantic Analysis and Symbolic Artificial Intelligence. J. Phys. A-Math. Gen. 132, L123–L132 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Diederik Aerts
    • 1
  • Sandro Sozzo
    • 1
  1. 1.Center Leo Apostel for Interdisciplinary StudiesVrije Universiteit BrusselBrusselsBelgium

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