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).
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).
We consider the following model of decision-making by cognitive systems. We present an algorithm -- quantum-like representation algorithm (QLRA) -- which provides a possibility to represent probabilistic data of any origin by complex probability amplitudes. Our conjecture is that cognitive systems developed the ability to use QLRA. They operate with complex probability amplitudes, mental wave functions. Since the mathematical formalism of QM describes as well (under some generalization) processing of such quantum-like (QL) mental states, the conventional quantum decision-making scheme can be used by the brain. We consider a modification of this scheme to describe decision-making in the presence of two ``incompatible'' mental variables. Such a QL decision-making can be used in situations like Prisoners Dilemma (PD) as well as others corresponding to so called disjunction effect in psychology and cognitive science.
This book deals with applications of quantum mechanical techniques to areas outside of quantum mechanics, so-called quantum-like modeling. Research in this area has grown over the last 15 years. But even already more than 50 years ago, the interaction between Physics Nobelist Pauli and the psychologist Carl Jung in the 1950's on seeking to find analogous uses of the complementarity principle from quantum mechanics in psychology needs noting. This book does NOT want to advance that society is quantum mechanical! The macroscopic world is manifestly not quantum mechanical. But this rules not out that one can use concepts and the mathematical apparatus from quantum physics in a macroscopic environment. A mainstay ingredient of quantum mechanics, is 'quantum probability' and this tool has been proven to be useful in the mathematical modelling of decision making. In the most basic experiment of quantum physics, the double slit experiment, it is known (from the works of A. Khrennikov) that the law of total probability is violated. It is now well documented that several decision making paradoxes in psychology and economics (such as the Ellsberg paradox) do exhibit this violation of the law of total probability. When data is collected with experiments which test 'non-rational' decision making behaviour, one can observe that such data often exhibits a complex non-commutative structure, which may be even more complex than if one considers the structure allied to the basic two slit experiment. The community exploring quantum-like models has tried to address how quantum probability can help in better explaining those paradoxes. Research has now been published in very high standing journals on resolving some of the paradoxes with the mathematics of quantum physics. The aim of this book is to collect the contributions of world's leading experts in quantum like modeling in decision making, psychology, cognition, economics, and finance.
The quantum cognition research programme concerns the application of quantum probability theory(the rules for how to assign probabilities to events from quantum mechanics, without the physics) tocognitive modeling. We review quantum cognitive models in several areas of psychology, includingconjunction/ disjunction fallacies in probabilistic judgment, conceptual combinations, similarity, order effects on judgments, causal inference, the disjunction effect in decision making, measurement and interference effects on judgments and decisions, memory, perception, and other judgment anddecision-making applications. For each area, we first present the empirical findings that have motivated the application of quantum models, emphasizing any characteristics which are particularly puzzling or have resisted coherent theoretical explanations previously; we then discuss the quantum cognitive models, noting the key features of the models that help explain the empirical data; we finally cast a critical eye on the models and explore comparisons with non-quantum models.
The article presents a review of foreign scientific literature on the quantum-like approach to understanding the modeling of cognition and decision-making processes. It is shown that the current application of quantum physics approaches to consciousness, psychological approaches such as perception, cognition, emotions, consciousness and learning, involves the search for a single objective mathematical model of what underlies the experience of the brain. The use of quantum physics algorithms can help in understanding the mechanisms of brain malfunctions and memory impairments that are found in pathologies such as dementia caused by Alzheimer's disease, schizophrenia, etc. Quantum physics approaches are applicable to issues of modeling cognition and decision-making processes, as well as in cognitive research, information processing by the human brain, artificial intelligence development, psychology, social and political sciences. Application of the abstract mathematical principles of quantum theory can help in understanding human consciousness and behavior. Quantum probability theory is applied to modeling human behavior due to the prevalence of uncertainty in human interaction with the world. Quantum cognitive models are especially useful in research in such areas as errors in decision making, order effects of questions, conceptual combinations, accumulation of evidence, perception, etc. Of particular interest to researchers are issues of quantum-like modeling of cognition and decision-making processes, the apparatus of quantum information and probability theory, useful for such modeling, as well as the use of such apparatus in cognitive research, the development of artificial intelligence, psychology, social and political sciences.
Quantum cognition, a growing topic at the interface of quantum physics and cognitive research, provides a new viewpoint on the intricacies of human thought processes. In contrast to classic Boolean algebraic models, which have long dominated cognitive psychology, quantum cognition proposes a new framework influenced by quantum mechanics' algebraic structure. This deviation derives from the understanding that natural notions, based on prototypes, are more closely related to convex sets than to the rigid rules of Boolean algebra. Drawing on the fundamental work of luminaries such as John von Neumann, quantum cognition reveals a unique probability theory based on ortho-algebras, challenging traditional probabilistic reasoning based on Boolean algebras. This change opens up solutions to complex challenges in rationality, logical thinking, and probabilistic reasoning, ushering in a new era of cognitive modelling. Several arguments in the literature support the importance of quantum cognition in explaining cognitive phenomena.
Classical models of decision-making under uncertainty, grounded in expected utility theory and Bayesian probability, often fail to account for systematic cognitive anomalies such as preference reversals, order effects, ambiguity aversion, and context-dependent choices. Quantum cognition models offer a novel theoretical framework that applies the mathematical principles of quantum probability—such as superposition, interference, and non-commutativity—to cognitive processes without assuming physical quantum mechanisms in the brain. By representing cognitive states as probabilistic superpositions that collapse through decision “measurements,” these models provide parsimonious explanations for violations of classical rationality. This paper examines how quantum cognition frameworks capture contextual influence, belief updating, and interference effects in uncertain decision environments. Drawing on findings from cognitive psychology and behavioral economics, the study highlights the relevance of quantum cognition for applications in economic choice modeling, legal decision analysis, and artificial intelligence. The analysis suggests that quantum probability offers a robust alternative to classical approaches when modeling human decision-making in complex, ambiguous, and context-sensitive situations.