Advertisement

Context and Interference Effects in the Combinations of Natural Concepts

  • Diederik Aerts
  • Jonito Aerts
  • Lester Beltran
  • Isaac Distrito
  • Massimiliano Sassoli de Bianchi
  • Sandro SozzoEmail author
  • Tomas Veloz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10257)

Abstract

The mathematical formalism of quantum theory exhibits significant effectiveness when applied to cognitive phenomena that have resisted traditional (set theoretical) modeling. Relying on a decade of research on the operational foundations of micro-physical and conceptual entities, we present a theoretical framework for the representation of concepts and their conjunctions and disjunctions that uses the quantum formalism. This framework provides a unified solution to the ‘conceptual combinations problem’ of cognitive psychology, explaining the observed deviations from classical (Boolean, fuzzy set and Kolmogorovian) structures in terms of genuine quantum effects. In particular, natural concepts ‘interfere’ when they combine to form more complex conceptual entities, and they also exhibit a ‘quantum-type context-dependence’, which are responsible of the ‘over- and under-extension’ that are systematically observed in experiments on membership judgments.

Keywords

Cognitive psychology Concept combination Context effects Interference effects Quantum modeling Quantum structures 

References

  1. 1.
    Rosch, E.: Natural categories. Cogn. Psychol. 4, 328–350 (1973)CrossRefGoogle Scholar
  2. 2.
    Rosch, E.: Principles of categorization. In: Rosch, E., Lloyd, B. (eds.) Cognition and Categorization, pp. 133–179. Lawrence Erlbaum, Hillsdale (1978)Google Scholar
  3. 3.
    Zadeh, L.: A note on prototype theory and fuzzy sets. Cognition 12, 291–297 (1982)CrossRefGoogle Scholar
  4. 4.
    Osherson, D., Smith, E.: On the adequacy of prototype theory as a theory of concepts. Cognition 9, 35–58 (1981)CrossRefGoogle Scholar
  5. 5.
    Hampton, J.A.: Overextension of conjunctive concepts: evidence for a unitary model for concept typicality and class inclusion. J. Exp. Psychol.: Learn. Mem. Cogn. 14, 12–32 (1988a)Google Scholar
  6. 6.
    Hampton, J.A.: Disjunction of natural concepts. Mem. Cogn. 16, 579–591 (1988b)CrossRefGoogle Scholar
  7. 7.
    Alxatib, S., Pelletier, J.: On the psychology of truth-gaps. In: Nouwen, R., Rooij, R., Sauerland, U., Schmitz, H.-C. (eds.) VIC 2009. LNCS, vol. 6517, pp. 13–36. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-18446-8_2 CrossRefGoogle Scholar
  8. 8.
    Kolmogorov, A.N.: Grundbegriffe der Wahrscheinlichkeitrechnung. Ergebnisse Der Mathematik (1933). Translated as Foundations of Probability (1950). Chelsea Publishing Company, New YorkGoogle Scholar
  9. 9.
    Aerts, D.: Quantum structure in cognition. J. Math. Psychol. 53, 314–348 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Aerts, D., Gabora, L.S., Sozzo, S.: Concepts and their dynamics: a quantum-theoretic modeling of human thought. Top. Cogn. Sci. 5, 737–772 (2013)Google Scholar
  11. 11.
    Busemeyer, J.R., Bruza, P.D.: Quantum Models of Cognition and Decision. Cambridge University Press, Cambridge (2012)CrossRefGoogle Scholar
  12. 12.
    Aerts, D., Broekaert, J., Gabora, L., Sozzo, S.: Quantum structure and human thought. Behav. Brain Sci. 36, 274–276 (2013)CrossRefGoogle Scholar
  13. 13.
    Pothos, E.M., Busemeyer, J.R.: Can quantum probability provide a new direction for cognitive modeling? Behav. Brain Sci. 36, 255–274 (2013)CrossRefGoogle Scholar
  14. 14.
    Haven, E., Khrennikov, A.: Quantum Social Science. Cambridge University Press, Cambridge (2013)CrossRefzbMATHGoogle Scholar
  15. 15.
    Wang, Z., Solloway, T., Shiffrin, R.M., Busemeyer, J.R.: Context effects produced by question orders reveal quantum nature of human judgments. Proc. Natl. Acad. Sci. 111, 9431–9436 (2014)CrossRefGoogle Scholar
  16. 16.
    Aerts, D., Sassoli de Bianchi, M., Sozzo, S.: On the foundations of the Brussels operational-realistic approach to cognition. Front. Phys. 4(17) (2015). doi: 10.3389/fphy.2016.00017
  17. 17.
    Aerts, D., Aerts, S.: Applications of quantum statistics in psychological studies of decision processes. Found. Sci. 1, 85–97 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Beltrametti, E.G., Cassinelli, G.: The Logic of Quantum Mechanics. Addison-Wesley, Reading (1981)zbMATHGoogle Scholar
  19. 19.
    Aerts, D.: Foundations of quantum physics: a general realistic and operational approach. Int. J. Theoret. Phys. 38, 289–358 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Hampton, J.A.: Conceptual combination: conjunction and negation of natural concepts. Mem. Cogn. 25, 888–909 (1997)CrossRefGoogle Scholar
  21. 21.
    Aerts, D., Sozzo, S., Veloz, T.: Quantum structure of negation and conjunction in human thought. Front. Psychol. (2015). doi: 10.3389/fpsyg.2015.01447
  22. 22.
    Aerts, D., Sozzo, S., Veloz, T.: New fundamental evidence of non-classical structure in the combination of natural concepts. Philos. Trans. R. Soc. A 374, 20150095 (2016)CrossRefGoogle Scholar
  23. 23.
    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)CrossRefzbMATHGoogle Scholar
  24. 24.
    Aerts, D., Gabora, L.: A theory of concepts and their combinations II: a hilbert space representation. Kybernetes 34, 192–221 (2005)CrossRefzbMATHGoogle Scholar
  25. 25.
    Aerts, D., Sassoli de Bianchi, M.: . Beyond-quantum modeling of question order effects and response replicability in psychological measurements. J. Math. Psych. (2015, to appear). arXiv:1508.03686[cs.AI]
  26. 26.
    Aerts, D.: Quantum interference and superposition in cognition: development of a theory for the disjunction of concepts. In: Aerts, D., et al. (eds.) Worldviews, Science and Us, pp. 169–211. World Scientific, Singapore (2011)CrossRefGoogle Scholar
  27. 27.
    Dirac, P.A.M.: Quantum Mechanics, 4th edn. Oxford University Press, London (1958)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Diederik Aerts
    • 1
  • Jonito Aerts
    • 2
  • Lester Beltran
    • 3
  • Isaac Distrito
    • 4
  • Massimiliano Sassoli de Bianchi
    • 1
    • 5
  • Sandro Sozzo
    • 6
    Email author
  • Tomas Veloz
    • 1
  1. 1.Center Leo Apostel for Interdisciplinary Studies (CLEA)Brussels Free University (VUB)BrusselBelgium
  2. 2.KASK and ConservatoryGhentBelgium
  3. 3.Tondo, ManilaThe Philippines
  4. 4.ManilaThe Philippines
  5. 5.Laboratorio di Autoricerca di BaseLuganoSwitzerland
  6. 6.School of Business and Research Centre IQSCSUniversity of LeicesterLeicesterUK

Personalised recommendations