Towards a Quantum Probability Theory of Similarity Judgments

  • James M. YearsleyEmail author
  • Emmanuel M. Pothos
  • James A. Hampton
  • Albert Barque Duran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8951)


We review recent progress in understanding similarity judgments in cognition by means of quantum probability theory (QP) models. We begin by outlining some features of similarity judgments that have proven difficult to model by traditional approaches. We then briefly present a model of similarity judgments based on QP, and show how it can solve many of the problems faced by traditional approaches. Finally we look at some areas where the quantum model is currently less satisfactory, and discuss some open questions and areas for further work.


Similarity Comparison Knowledge State Quantum Model Concept Space Quantum Probability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



E.M.P. and J.M.Y. were supported by Leverhulme Trust grant no. RPG-2013-00. Further, E.M.P. was supported by Air Force Office of Scientific Research (AFOSR), Air Force Material Command, USAF, grants no. FA 8655-13-1-3044. The US Government is authorized to reproduce and distribute reprints for Governmental purpose notwithstanding any copyright notation thereon.


  1. Aerts, D., Gabora, L.: A theory of concepts and their combinations II: a Hilbert space representation. Kybernetes 34, 192–221 (2005)CrossRefzbMATHGoogle Scholar
  2. Aerts, S., Kitto, K., Sitbon, L.: Similarity metrics within a point of view. In: Song, D., Melucci, M., Frommholz, I., Zhang, P., Wang, L., Arafat, S. (eds.) QI 2011. LNCS, vol. 7052, pp. 13–24. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  3. Ashby, G.F., Perrin, N.A.: Towards a unified theory of similarity and recognition. Psychol. Rev. 95, 124–150 (1988)CrossRefGoogle Scholar
  4. Atmanspacher, H., Romer, H., Wallach, H.: Weak quantum theory: formal framework and selected applications. Weak quantum theory: complementarity and entanglement in physics and beyond. Found. Phys. 32, 379–406 (2006)CrossRefGoogle Scholar
  5. Bowdle, B.F., Medin, D.L.: Reference-point reasoning and comparison asymmetries. In: Moore, J.D., Stenning, K. (eds.) Proceedings of the 23rd Annual Conference of the Cognitive Science Society, pp. 116–121. Psychology Press, New York (2001)Google Scholar
  6. Busemeyer, J.R., Bruza, P.: Quantum Models of Cognition and Decision Making. Cambridge University Press, Cambridge (2011)Google Scholar
  7. Busemeyer, J.R., Pothos, E.M., Franco, R., Trueblood, J.: A quantum theoretical explanation for probability judgment errors. Psychol. Rev. 118, 193–218 (2011)CrossRefGoogle Scholar
  8. De Deyne, S., Verheyen, S., Ameel, E., Vanpaemel, W., Dry, M.J., Voorspoels, W., Storms, G.: Exemplar by feature applicability matrices and other Dutch normative data for semantic concepts. Behav. Res. Meth. 40, 1030–1048 (2008)CrossRefGoogle Scholar
  9. Goldstone, R.L.: The role of similarity in categorization: providing a groundwork. Cognition 52, 125–157 (1994)CrossRefGoogle Scholar
  10. Goodman, N.: Seven strictures on similarity. In: Goodman, N. (ed.) Problems and Projects, pp. 437–447. Bobbs-Merrill, Indianapolis (1972)Google Scholar
  11. Griffiths, R.B.: Consistent Quantum Theory. Cambridge University Press, Cambridge (2002)zbMATHGoogle Scholar
  12. Jones, M.N., Gruenenfelder, T.M., Recchia, G.: In defense of spatial models of lexical semantics. In: Carlson, L., Hlscher, C., Shipley, T. (eds.) Proceedings of the 33rd Annual Conference of the Cognitive Science Society, pp. 3444–3449. Cognitive Science Society, Austin (2011)Google Scholar
  13. Khrennikov, A.Y.: Ubiquitous Quantum Structure: From Psychology to Finance. Springer, Berlin (2010)CrossRefGoogle Scholar
  14. Michelbacher, L., Evert, S., Schtze, H.: Asymmetry in corpus-derived and human word associations. Corpus Linguist. Linguist. Theor. 7(2), 245–276 (2011)CrossRefGoogle Scholar
  15. Nosofsky, R.M.: Choice, similarity, and the context theory of classification. J. Exp. Psychol. Learn. Mem. Cogn. 10, 104–114 (1984)CrossRefGoogle Scholar
  16. Parducci, A.: Category judgment: a range-frequency model. Psychol. Rev. 72, 407–418 (1965)CrossRefGoogle Scholar
  17. Polk, T.A., Behensky, C., Gonzalez, R., Smith, E.E.: Rating the similarity of simple perceptual stimuli: asymmetries induced by manipulating exposure frequency. Cognition 82, B75–B88 (2002)CrossRefGoogle Scholar
  18. Pothos, E.M.: The rules versus similarity distinction. Behav. Brain Sci. 28, 1–49 (2005)Google Scholar
  19. Pothos, E.M., Busemeyer, J.R., Trueblood, J.S.: A quantum geometric model of similarity. Psychol. Rev. 120, 679–696 (2013)CrossRefGoogle Scholar
  20. Rosch, E.: Cognitive reference points. Cogn. Psychol. 7, 532–547 (1975)CrossRefGoogle Scholar
  21. Trueblood, J.S., Brown, S.D., Heathcote, A., Busemeyer, J.R.: Not just for consumers: context effects are fundamental to decision-making. Psychol. Sci. 24(6), 901–908 (2013)CrossRefGoogle Scholar
  22. Tversky, A.: Features of similarity. Psychol. Rev. 84, 327–352 (1977)CrossRefGoogle Scholar
  23. Yearsley, J.M., Pothos, E.M., Hampton, J.A., Barque Duran, A.: Context effects in similarity judgments (in preparation)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • James M. Yearsley
    • 1
    Email author
  • Emmanuel M. Pothos
    • 1
  • James A. Hampton
    • 1
  • Albert Barque Duran
    • 1
  1. 1.Department of PsychologyCity University LondonLondonUK

Personalised recommendations