Quantum models of cognition and decision

Abstract The purpose of this article is to discuss principle ideas of quantum cognition research program, which comprise elements of the formalism of quantum mechanics (mainly Hilbert space theory and quantum probability theory) for modeling human cognition and decision processes. In the opinion of authors of this program, paradox empirical findings in psychological literature may be explained based on concepts of quantum mechanics. Formally, there is described a discrete-time random chain χ which is defined on a finite interval [0, T] and χ(t) can assume only finite number of values. The space H of such processes will be finite-dimensioned. Then some properties and applications of the quantum probability space on H are studied.

[1]  A. R. Marlow,et al.  Mathematical foundations of quantum theory , 1978 .

[2]  W. Bean.  Physics and Philosophy, the Revolution in Modern Science. , 1959 .

[3]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

[4]  Diederik Aerts,et al.  Quantum Structure in Cognition: Fundamentals and Applications , 2011, ArXiv.

[5]  A. Gleason.  Measures on the Closed Subspaces of a Hilbert Space , 1957 .

[6]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[7]  N. Mukunda,et al.  The Character of Physical Law , 2018 .

[8]  A. Tversky,et al.  Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment , 1983 .

[9]  D. Spalding.  The Principles of Psychology , 1873, Nature.

[10]  Jerome R. Busemeyer,et al.  A Quantum Question Order Model Supported by Empirical Tests of an A Priori and Precise Prediction , 2013, Top. Cogn. Sci..

[11]  A. Tversky,et al.  Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment , 1983 .

[12]  A. N. Kolmogorov,et al.  Foundations of the theory of probability , 1960 .

[13]  Jerome R. Busemeyer,et al.  Quantum Models of Cognition and Decision , 2012 .

[14]  Harald Atmanspacher,et al.  The Potential of Using Quantum Theory to Build Models of Cognition , 2013, Top. Cogn. Sci..

[15]  Diederik Aerts,et al.  Quantum Interference in Cognition: Structural Aspects of the Brain , 2012, ArXiv.

[16]  W. Heitler.  The Principles of Quantum Mechanics , 1947, Nature.