Modeling of quantum-like cognitive phenomena by the Fourier-holography technique under the choice of alternatives

The article is dedicated to the search for a biologically motivated mechanism of the cognitive phenomenon of violation of the classical formula of total probability for the disjunction of incompatible events, which is considered by a number of researchers as a quantum-like phenomenon. A classical mechanism implemented by the 6f Fourier holography scheme of the resonant architecture that does not require reference to quantum mechanics either in its physical nature or at the level of formalism is demonstrated. In the analysis, the decision-making is interpreted as a choice of alternatives by using the non-cooperative game "Prisoner's Dilemma". The approach to the task is based on the search for a mechanism for forming a conditional estimate under a condition that contradicts the rule of monotonous decision logic. It is demonstrated that this estimate, in contrast to the unconditional and conditional one with a non-contradictory condition, is formed by logic with exception. The ring architecture of the holographic setup corresponds to the biologically inspired neural network concept of the excitation ring and implements cognitive dissonance on logic with exception. Conditions and ranges of violation of the classical formula of total probability in relation to the correlation radius of the reference image recorded in a hologram storing the monotone logic inference rule are analytically determined. The analytical model is confirmed by a quantitative coincidence of the results of numerical modeling with the published results of natural experiments.

Generalized Fock space and contextuality

This paper is devoted to linear space representations of contextual probabilities—in generalized Fock space. This gives the possibility to use the calculus of creation and annihilation operators to express probabilistic dynamics in the Fock space (in particular, the wide class of classical kinetic equations). In this way, we reproduce the Doi–Peliti formalism. The context-dependence of probabilities can be quantified with the aid of the generalized formula of total probability—by the magnitude of the interference term. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond'.

Quantum Bayesianism as the basis of general theory of decision-making

We discuss the subjective probability interpretation of the quantum-like approach to decision making and more generally to cognition. Our aim is to adopt the subjective probability interpretation of quantum mechanics, quantum Bayesianism (QBism), to serve quantum-like modelling and applications of quantum probability outside of physics. We analyse the classical and quantum probabilistic schemes of probability update, learning and decision-making and emphasize the role of Jeffrey conditioning and its quantum generalizations. Classically, this type of conditioning and corresponding probability update is based on the formula of total probability—one the basic laws of classical probability theory.