A case for applying an abstracted quantum formalism to cognition

New Ideas in Psychology

Volumn 29, Issue 2, 2011, Pages 136-146

  Aerts, Diederik ^a   Broekaert, Jan ^a   Gabora, Liane ^b  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Concepts; Consciousness; Contextuality; Decision making; Liar paradox; Quantum

Indexed keywords

EID: 78649747778     PISSN: 0732118X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.newideapsych.2010.06.002     Document Type: Article

References (66)

1. Accardi L. Foundations of quantum probability. Rendiconti del Seminario Matematico dell'Università e del Politecnico, Torino 1982, 249-270.
2. Accardi L., Fedullo A. On the statistical meaning of complex numbers in quantum mechanics. Lettere al Nuovo Cimento 1982, 34:161-172.
3. Aerts D. Description of many physical entities without the paradoxes encountered in quantum mechanics. Foundations of Physics 1982, 12:1131-1170.
4. Aerts D. Classical theories and nonclassical theories as a special case of a more general theory. Journal of Mathematical Physics 1983, 24:2441-2453.
5. Aerts D. A possible explanation for the probabilities of quantum mechanics. Journal of Mathematical Physics 1986, 27:202-210.
6. Aerts D. The origin of the non-classical character of the quantum probability model. Information, complexity, and control in quantum physics 1987, 77-100. Springer-Verlag, Vienna. A. Blanquiere, S. Diner, G. Lochak (Eds.).
7. Aerts D. Quantum structures due to fluctuations of the measurement situations. International Journal of Theoretical Physics 1993, 32:2207-2220.
8. Aerts D. Quantum structures: an attempt to explain their appearance in nature. International Journal of Theoretical Physics 1995, 34:1165-1186. URL. http://uk.arxiv.org/abs/quant-ph/0111071.
9. Aerts D. Foundations of quantum physics: a general realistic and operational approach. International Journal of Theoretical Physics 1998, 38:289-358.
10. Aerts D. Being and change: foundations of a realistic operational formalism. Probing the structure of quantum mechanics: Nonlinearity, nonlocality, probability and axiomatics 2002, 71-110. World Scientific, Singapore. D. Aerts, M. Czachor, T. Durt (Eds.).
11. Aerts D. Quantum structure in cognition. Journal of Mathematical Psychology 2009, 53:314-348.
12. Aerts D., Aerts S. Applications of quantum statistics in psychological studies of decision processes. Foundations of Science 1994, 1:85-97.
13. Aerts D., Aerts S. Applications of quantum statistics in psychological studies of decision processes. Topics in the foundation of statistics 1997, 85-97. Kluwer, Dordrecht. B. van Fraassen (Ed.).
14. Aerts D., Aerts S., Broekaert J., Gabora L. The violation of Bell inequalities in the macroworld. Foundations of Physics 2000, 30:1387-1414. URL. http://uk.arxiv.org/abs/quant-ph/0007044.
15. Aerts D., Aerts S., Durt T., Leveque O. Classical and quantum probability in the epsilon model. International Journal of Theoretical Physics 1999, 38:407-429. (this is now Aerts et al. 1999, page 16 on top).
16. Aerts D., Aerts S., Gabora L. Experimental evidence for quantum structure in cognition. Proceedings of QI 2009-Third international symposium on quantum interaction. Lecture notes in computer science 2009, Vol. 5494:59-70. Springer, Berlin.
17. Aerts D., Broekaert J., Smets S. A quantum structure description of the liar paradox. International Journal of Theoretical Physics 1999, 38:3231-3239. URL. http://uk.arxiv.org/abs/quant-ph/0106131.
18. Aerts D., Broekaert J., Smets S. The liar paradox in a quantum mechanical perspective. Foundations of Science 1999, 4:115-132. URL. http://uk.arxiv.org/abs/quant-ph/0007047.
19. Aerts D., D'Hooghe B. Classical logical versus quantum conceptual thought: examples in economics, decision theory and concept theory. Proceedings of QI 2009-third international symposium on quantum interaction. Lecture notes in computer science 2009, Vol. 5494:128-142. Springer, Berlin.
20. Aerts D., Czachor M. Quantum aspects of semantic analysis and symbolic artificial intelligence. Journal of Physics A-Mathematical and General 2004, 37:L123-L132.
21. Aerts D., Czachor M. Tensor-product vs. geometric-product coding. Physical Review A 2008, 77:012316.
22. Aerts D., Czachor M., de Moor B. Geometric analogue of holographic reduced representation. Journal of Mathematical Psychology 2009, 53:389-398.
23. Aerts D., Durt T., van Bogaert B. A physical example of quantum fuzzy sets and the classical limit. Tatra Mountains Mathematical Publications 1993, 1:5-15.
24. Aerts D., Durt T. Quantum, classical, and intermediate: an illustrative example. Foundations of Physics 1994, 24:1353-1369.
25. Aerts D., Durt T. Quantum, classical and intermediate: a measurement model. Symposium on the foundations of modern physics 1994, Éditions Frontières, Gif-sur-Yvettes, France. K.V. Laurikainen, C. Montonen, K. Sunnarborg (Eds.).
26. Aerts D., Gabora L. A theory of concepts and their combinations I: the structure of the sets of contexts and properties. Kybernetes 2005, 34:167-191. URL. http://uk.arxiv.org/abs/quant-ph/0402207.
27. Aerts D., Gabora L. A theory of concepts and their combinations II: a Hilbert space representation. Kybernetes 2005, 34:192-221. URL. http://uk.arxiv.org/abs/quant-ph/0402205.
28. Bar-Hillel M., Neter E. How alike is it? Versus how likely is it?: a disjunction fallacy in probability judgments. Journal of Personality and Social Psychology 1986, 65:1119-1131.
29. Barrett L.F., Tugade M.M., Engle R.W. Individual differences in working memory capacity and dual-process theories of the mind. Psychological Bulletin 2004, 130:553-573.
30. Bell J.S. On the Einstein Podolsky Rosen paradox. Physics 1964, 1:195-200.
31. Blei D.M., Ng A.N., Jordan M.I., Lafferty J. Latent Dirichlet allocation. Journal of Machine Learning Research 2003, 3:993-1022.
32. Broekaert J., Aerts D., D'Hooghe B. The generalized Liar Paradox: a quantum model and interpretation. Foundations of Science 2002, 11:399-418.
33. Bruza P.D., Cole R.J. Quantum logic of semantic space: an exploratory investigation of context effects in practical reasoning. We will show them: Essays in honour of Dov Gabbay 2005, College Publications, London. S. Artemov, H. Barringer, A.S. d'Avila Garcez, L.C. Lamb, J. Woods (Eds.).
34. Proceedings of the AAAI spring symposium on quantum interaction 2007, AAAI Press, Menlo Park, CA. P.D. Bruza, W. Lawless, C.J. van Rijsbergen, D. Sofge (Eds.).
35. Quantum interaction: Proceedings of the second quantum interaction symposium 2008, College Publications, London. P.D. Bruza, W. Lawless, C.J. van Rijsbergen, D. Sofge (Eds.).
36. Proceedings of the third quantum interaction symposium. Lecture notes in artificial intelligence, 5494 2009, Springer, Berlin, Heidelberg. P.D. Bruza, D. Sofge, W. Lawless, C.J. van Rijsbergen, M. Klusch (Eds.).
37. Busemeyer J.R., Wang Z., Townsend J.T. Quantum dynamics of human decision making. Journal of Mathematical Psychology 2006, 50:220-241.
38. Deerwester S., Dumais S.T., Furnas G.W., Landauer T.K., Harshman R. Indexing by latent semantic analysis. Journal of the American Society for Information Science 1990, 41:391-407.
39. Edelman G.M., Tononi G. A universe of consciousness: How matter becomes imagination 2000, Basic Books, New York.
40. Gabora, L. (2001). Cognitive mechanisms underlying the origin and evolution of culture. Doctoral dissertation. Belgium: Léo Apostel Centre for Interdisciplinary Studies, Free University of Brussels.
41. Gabora L., Aerts D. Contextualizing concepts using a mathematical generalization of the quantum formalism. Journal of Experimental and Theoretical Artificial Intelligence 2002, 14(4):327-358.
42. Gabora L., Aerts D. Evolution as context-driven actualization of potential. Interdisciplinary Science Reviews 2005, 30:69-88.
43. Gabora L., Rosch E., Aerts D. Toward an ecological theory of concepts. Ecological Psychology 2008, 20:84-116.
44. Gaussier E., Goutte C., Popat K., Chen F. A hierarchical model for clustering and categorising documents. Advances in information retrieval. Lecture notes in computer science 2002, Vol. 2291. Springer, Berlin.
45. Griffiths T.L., Steyvers M. Prediction and semantic association. Advances in Neural Information Processing Systems 2002, URL. http://books.nips.cc/nips15.html.
46. Hofmann T. Probabilistic latent semantic analysis. Proceedings of uncertainty in artificial intelligence 1999, UAI'99, Stockholm.
47. Lambert Mogiliansky A., Zamir S., Zwirn H. Type indeterminacy: a model of the KT(Kahneman-Tversky)-man. Journal of Mathematical Psychology 2009, 53:349-361.
48. Landauer T.K., Dumais S.T. Solution to Plato's problem: the latent semantic analysis theory of acquisition, induction and representation of knowledge. Psychological Review 1977, 104:211-240.
49. Landauer T.K., Foltz P.W., Laham D. Introduction to latent semantic analysis. Discourse Processes 1998, 25:259-284.
50. Li Y., Cunningham H. Geometric and quantum methods for information retrieval. ACM SIGIR 2008, 42:22-32.
51. Lund K., Burgess C. Producing high-dimensional semantic spaces from lexical co-occurrence. Behavior Research Methods, Instruments and Computers 1990, 28:203-208.
52. Paivio A. Mind and its evolution: A dual coding theoretical approach 2007, Erlbaum, Mahwah, NJ.
53. Pitowsky I. Quantum probability - Quantum logic 1989, Springer, New York.
54. Plate T.A. Holographic reduced representations. IEEE Transactions on Neural Networks 1995, 6:623-641.
55. Plate T.A. Holographic reduced representation: Distributed representation for cognitive structures 2003, University of Chicago Press, Chicago.
56. Pothos, E. M., & Busemeyer, J. R. (2009). A quantum probability model explanation for violations of " rational" decision theory. Proceedings of the Royal Society, B.
57. van Rijsbergen K. The geometry of information retrieval 2004, Cambridge University Press, Cambridge.
58. Salton G., Wong A., Yang C.S. A vector space model for automatic indexing. Communications of the ACM 1975, 18:613-620.
59. Sloman S.A. The empirical case for two systems of reasoning. Psychological Bulletin 1996, 119:3-22.
60. Sun R. Duality of the mind 2002, Erlbaum, Mahwah, NJ.
61. Tversky A., Kahneman D. Judgments of and by representativeness. Judgment under uncertainty: Heuristics and biases 1982, Cambridge University Press, Cambridge. D. Kahneman, P. Slovic, A. Tversky (Eds.).
62. Tversky A., Kahneman D. Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review 1983, 90:293-315.
63. Tversky A., Shafir E. The disjunction effect in choice under uncertainty. Psychological Science 1992, 3:305-309.
64. Vinokourov A., Girolami M. A probabilistic framework for the hierarchic organisation and classification of document collections. Journal of Intelligent Information Systems 2002, 18:153-172.
65. Widdows D. Orthogonal negation in vector spaces for modeling word-meanings and document retrieval. Proceedings of the 41st annual meeting of the association for computational linguistics 2003, 136-143.
66. Widdows D., Peters S. Word vectors and quantum logic: experiments with negation and disjunction. Mathematics of Language 2003, 8:141-154.