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Cited by 16Quantum Mechanics and ApplicationsAdvanced Algebra and LogicLogic, Reasoning, and Knowledge

Nondistributivity of human logic and violation of response replicability effect in cognitive psychology

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Ozawa, Masanao, Khrennikov, Andrei·2023·Journal of Mathematical Psychology
DOI 10.1016/j.jmp.2022.102739
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Abstract

The aim of this paper is to promote quantum logic as one of the basic tools for analyzing human reasoning. We compare it with classical (Boolean) logic and highlight the role of violation of the distributive law for conjunction and disjunction. It is well known that nondistributivity is equivalent to incompatibility of logical variables — the impossibility to assign jointly the two-valued truth values to these variables. A natural question arises as to whether quantum logical nondistributivity in human logic can be tested experimentally. We show that testing the response replicability effect (RRE) in cognitive psychology is equivalent to testing nondistributivity — under the prevailing conjecture that the mental state update generated by observation is described as orthogonal projection of the mental state vector (the projective update conjecture of Wang and Busemeyer). A simple test of RRE is suggested. In contrast to the previous works in quantum-like modeling, we proceed in the state-dependent framework; in particular, distributivity, compatibility, and RRE are considered in a fixed mental state. In this framework, we improve the previous result on the impossibility to combine question order and response replicability effects by using (von Neumann–Lüders) projective measurements.

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Crossref · 10.1016/j.jmp.2022.102739

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  • In QPT, sequential joint probability exhibits QOE if and only if it does not exhibit RRE.

    “Conversely, in QPT, sequential joint probability exhibits QOE if and only if it does not exhibit RRE (Khrennikov et al., 2014; Ozawa & Khrennikov, 2023).”

    From Coupling quantum-like cognition with the neuronal networks within generalized probability theory (2025) · cites this paper as Ozawa & Khrennikov, 2023

    The Introduction (p. 4) says QOE and RRE are mutually exclusive only under the projective update conjecture. The Concluding Remarks (p. 13) explicitly say the authors’ model satisfies both QOE and RRE, contrary to the unqualified claim; the paper also does not establish that failure of RRE implies QOE. (LLM, conf=0.90)

    Checked by a reasoning model — may be wrong.

    Experimental — accuracy not yet measured

  • Sequential joint probability in CPT exhibits the response replicability effect but not the question order effect.

    “Regarding the question order effect (QOE) and the response replicability effect (RRE), sequential joint probability in CPT exhibits RRE but not QOE.”

    From Coupling quantum-like cognition with the neuronal networks within generalized probability theory (2025) · cites this paper as Ozawa & Khrennikov, 2023

    Section 6.2 (p. 11) shows that RRE holds for projective measurements when the relevant propositions are distributive. The Introduction (p. 4) says that RRE and QOE are mutually exclusive under the projective-update conjecture. These passages support the claimed relationship, but only under that measurement assumption; they do not establish it as an unconditional property of sequential joint probability in classical probability theory (CPT). (LLM, conf=0.82)

    Experimental — accuracy not yet measured

  • Such a model exists within the framework of GPT or through QPT combined with instrument theory for state updates.

    “We have demonstrated that such a model exists within the framework of GPT or through QPT combined with instrument theory for state updates (Ozawa & A., 2021; Ozawa & Khrennikov, 2023).”

    From Coupling quantum-like cognition with the neuronal networks within generalized probability theory (2025) · cites this paper as Ozawa & Khrennikov, 2023

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Cites

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Research works printed but not linked: 15

  1. [2][2] G. Boole, An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities . Macmillan, (1958[1854]).Reprinted with corrections, Dover Publications, New York, NY (reissued by Cambridge University Press, 2009). -
  2. [4][4] Kalmbach, G. Orthomodular lattices . Academic Press, London, New York, 1983. -
  3. [6][6] von Neumann, J. Mathematical Foundations of Quantum Mechanics (Princeton UP, Princeton, NJ, 1955). [Originally published: Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932)]. -
  4. [12][12] M. Ozawa, Quantum measurement theory for systems with finite dimensional state spaces, to appear in The Quantum-Like Revolution: A Festschrift in Honor of Professor Andrei Khrennikov , edited by E. Haven and A. Plotnitsky (Springer, Switzerland). https://arxiv.org/abs/2110.03219. - · arXiv
  5. [14][14] Khrennikov, A. (2010). Ubiquitous quantum structure: from psychology to finances . BerlinHeidelberg-New York: Springer. -
  6. [15][15] Busemeyer, J. and Bruza, P.(2012). Quantum models of cognition and decision. Cambridge: Cambridge Univ. Press. -
  7. [16][16] Bagarello, F. (2019). Quantum concepts in the social, ecological and biological sciences . Cambridge: Cambridge Unive. Press. -
  8. [17][17] Haven, E. and Khrennikov, A. (2013). Quantum social science . Cambridge: Cambridge Univ. Press. -
  9. [21][21] Basieva, I., Cervantes, V . H., Dzhafarov, E. N., and Khrennikov, A. (2019). True contextuality beats direct influences in human decision making. J. Exp. Psych.: General , 148(11), 1925. -
  10. [23][23] Basieva, I., Pandey, V., and Khrennikova, P. (2022). More Causes Less Effect: Destructive Interference in Decision Making. Entropy , 24(5), 725. ' -
  11. [26][26] Basieva, I. and Khrennikov, A. (2015). On the possibility to combine the order effect with sequential reproducibility for quantum measurements. Found. Physics , 45 (10), 1379-1393. -
  12. [27][27] Busemeyer, J. and Wang, (2017). Is there a problem with quantum models of psychological measurements? PLOS ONE , 12 (11), e0187733. -
  13. [32][32] Wang, Z., Solloway, T., Shiffrin, R. M. and Busemeyer, J. R. Context effects produced by question orders reveal quantum nature of human judgments. Proc. Natl. Acad. Sci. U.S.A. 111 , 9431-9436 (2014). -
  14. [40][40] Bruns, G. and Kalmbach, G. Some remarks on free orthomodular lattices. In Schmidt, J. (ed.) Proc. Lattice Theory Conf. , 397-408 (Houston, U.S.A., 1973). -
  15. [41][41] Takeuti, G. Quantum set theory. In Beltrametti, E. and van Frassen, B. C. (eds.) Current Issues in Quantum Logic , 303-322 (Plenum, New York, 1981). -

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Authors
Ozawa, M., & Khrennikov, A.
Affiliations
  • Chubu University (JP)
  • Linnaeus University (SE)
Corresponding author
Khrennikov, Andrei
ORCID
Venue
Journal of Mathematical Psychology
Publisher
Elsevier BV
Published
2023-02
Volume
112
Pages
102739
ISSN
0022-2496 (ISSN-L)
DOI
10.1016/j.jmp.2022.102739
OpenAlex
W4312109366
Cited by
16
References
1
Citations by year
2026: 8 · 2025: 4 · 2024: 1 · 2023: 3
FWCI
0.82
Type
journal article
Language
en
Open access
Licence
Locations
  • Journal of Mathematical Psychology (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DiVA (Linnaeus University) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Funders
Japan Society for the Promotion of Science (JP19H04066, JP21K11764, JP22K03424)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Algebra and Logic
  • Physical Sciences › Computer Science › Artificial Intelligence › Logic, Reasoning, and Knowledge
Keywords
quantum logic, human reasoning, Boolean logic, distributivity, orthogonal projection, question order effects

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