We present a quantum-like (QL) model in that contexts (complexes of e.g. mental, social, biological, economic or even political conditions) are represented by complex probability amplitudes. This approach gives the possibility to apply the mathematical quantum formalism to probabilities induced in any domain of science. In our model quantum randomness appears not as irreducible randomness (as it is commonly accepted in conventional quantum mechanics, e.g., by von Neumann and Dirac), but as a consequence of obtaining incomplete information about a system. We pay main attention to the QL description of processing of incomplete information. Our QL model can be useful in cognitive, social and political sciences as well as economics and artificial intelligence. In this paper we consider in a more detail one special application -- QL modeling of brain's functioning. The brain is modeled as a QL-computer.
We present a quantum-like (QL) model in that contexts (complexes of e.g. mental, social, biological, economic or even political conditions) are represented by complex probability amplitudes. This approach gives the possibility to apply the mathematical quantum formalism to probabilities induced in any domain of science. In our model quantum randomness appears not as irreducible randomness (as it is commonly accepted in conventional quantum mechanics, e.g., by von Neumann and Dirac), but as a consequence of obtaining incomplete information about a system. We pay main attention to the QL description of processing of incomplete information. Our QL model can be useful in cognitive, social and political sciences as well as economics and artificial intelligence. In this paper we consider in a more detail one special application -- QL modeling of brain's functioning. The brain is modeled as a QL-computer.
We present a quantum-like model in that contexts (com-plexes of physical, mental, or social conditions) are rep-resented by complex probability amplitudes. This ap-proach gives the possibility to apply the quantum for-malism for probabilities induced in any domain of sci-ence. In this paper we propose a model of brain func-tioning based on the quantum-like (QL) representation of mental contexts. In this model brain can be con-sidered as a QL (but not conventional quantum) com-puter. We discuss a possible mechanism of the QL-representation of information in the brain. It is based on processing of information at two different time scales: pre-cognitive (fine) and cognitive (coarse).
We propose a {\it quantum-like} (QL) model of the functioning of the brain. It should be sharply distinguished from the reductionist {\it quantum} model. By the latter cognition is created by {\it physical quantum processes} in the brain. The crucial point of our modelling is that discovery of the mathematical formalism of quantum mechanics (QM) was in fact discovery of a very general formalism describing {\it consistent processing of incomplete information} about contexts (physical, mental, economic, social). The brain is an advanced device which developed the ability to create a QL representation of contexts. Therefore its functioning can also be described by the mathematical formalism of QM. The possibility of such a description has nothing to do with composing of the brain of quantum systems (photons, electrons, protons,...). Moreover, we shall propose a model in that the QL representation is based on conventional neurophysiological model of the functioning of the brain. The brain uses the QL rule (given by von Neumann trace formula) for calculation of {\it approximative averages} for mental functions, but the physical basis of mental functions is given by neural networks in the brain. The QL representation has a {\it temporal basis.} Any cognitive process is based on (at least) two time scales: subcognitive time scale (which is very fine) and cognitive time scale (which is essentially coarser).
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.
We present a contextualist statistical realistic model for quantum-like representations in physics, cognitive science and psychology. We apply this model to describe cognitive experiments to check quantum-like structures of mental processes. The crucial role is played by interference of probabilities for mental observables. Recently one of such experiments based on recognition of images was performed. This experiment confirmed our prediction on quantum-like behaviour of mind. In our approach ``quantumness of mind'' has no direct relation to the fact that the brain (as any physical body) is composed of quantum particles. We invented a new terminology ``quantum-like (QL) mind.'' Cognitive QL-behaviour is characterized by nonzero coefficient of interference λ. This coefficient can be found on the basis of statistical data. There is predicted not only cosθ-interference of probabilities, but also hyperbolic coshθ-interference. This interference was never observed for physical systems, but we could not exclude this possibility for cognitive systems. We propose a model of brain functioning as QL-computer (there is discussed difference between quantum and QL computers).
The aim of this review is to highlight the possibility of applying the mathematical formalism and methodology of quantum theory to model behavior of complex biosystems, from genomes and proteins to animals, humans, and ecological and social systems. Such models are known as quantum-like, and they should be distinguished from genuine quantum physical modeling of biological phenomena. One of the distinguishing features of quantum-like models is their applicability to macroscopic biosystems or, to be more precise, to information processing in them. Quantum-like modeling has its basis in quantum information theory, and it can be considered one of the fruits of the quantum information revolution. Since any isolated biosystem is dead, modeling of biological as well as mental processes should be based on the theory of open systems in its most general form-the theory of open quantum systems. In this review, we explain its applications to biology and cognition, especially theory of quantum instruments and the quantum master equation. We mention the possible interpretations of the basic entities of quantum-like models with special interest given to QBism, as it may be the most useful interpretation.
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.