Quantum-like modeling of cognition
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This paper begins with a historical review of the mutual influence of physics and psychology, from Freud's invention of psychic energy inspired by von Boltzmann' thermodynamics to the enrichment quantum physics gained from the side of psychology by the notion of complementarity (the invention of Niels Bohr who was inspired by William James), besides we consider the resonance of the correspondence between Wolfgang Pauli and Carl Jung in both physics and psychology. Then we turn to the problem of development of mathematical models for laws of thought starting with Boolean logic and progressing towards foundations of classical probability theory. Interestingly, the laws of classical logic and probability are routinely violated not only by quantum statistical phenomena but by cognitive phenomena as well. This is yet another common feature between quantum physics and psychology. In particular, cognitive data can exhibit a kind of the probabilistic interference effect. This similarity with quantum physics convinced a multi-disciplinary group of scientists (physicists, psychologists, economists, sociologists) to apply the mathematical apparatus of quantum mechanics to modeling of cognition. We illustrate this activity by considering a few concrete phenomena: the order and disjunction effects, recognition of ambiguous figures, categorization-decision making. In Appendix 1 we briefly present essentials of theory of contextual probability and a method of representations of contextual probabilities by complex probability amplitudes (solution of the ``inverse Born's problem'') based on a quantum-like representation algorithm (QLRA).
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Order effects, conjunction and disjunction fallacies, and other context-dependent phenomena cannot be fully captured by classical probabilistic models but are naturally accommodated within quantum probability through interference and contextuality.
“These include order effects, conjunction and disjunction fallacies, and other context-dependent phenomena that cannot be fully captured by classical probabilistic models but are naturally accommodated within quantum probability through interference and contextuality [45].”
From Quantum-Inspired and Non-Classical Approaches to Consciousness: Models, Evidence and Constraints (2026) · cites this paper as [45]
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“In contrast, quantum-like approaches adopt the mathematical structure of quantum theory—particularly Hilbert space representations and quantum probability—to model cognitive phenomena without assuming that the brain operates as a quantum physical system [45].”
Influential
- Authors
- Khrennikov, A.
- Affiliations
- Linnaeus University (SE)
- Corresponding author
- Khrennikov, Andrei
- ORCID
- Khrennikov, Andrei
- Venue
- Frontiers in Physics
- Publisher
- Frontiers Media SA
- Published
- 2015-09-22
- Volume
- 3
- ISSN
- 2296-424X (ISSN-L)
- OpenAlex
- W2198371489
- Cited by
- 91
- References
- 91
- Citations by year
- 2026: 19 · 2025: 12 · 2024: 4 · 2023: 6 · 2022: 12 · 2021: 10 · 2020: 6 · 2019: 4 · 2018: 7 · 2017: 5 · 2016: 5 · 2015: 1
- FWCI
- 3.05
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- cc-by
- Locations
- Frontiers in Physics (publishedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Life Sciences › Neuroscience › Cognitive Neuroscience › Cognitive Science and Education Research
- Physical Sciences › Computer Science › Artificial Intelligence › Cognitive Computing and Networks
- Keywords
- quantum cognition, laws of thought, Boolean logic, classical probability, order effects, disjunction effect, contextual probability, complementarity, Niels Bohr, William James, Wolfgang Pauli, Carl Jung
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