Contextuality Analysis of Impossible Figures

Measures of contextuality in cyclic systems and the negative probabilities measure CNT3

Several principled measures of contextuality have been proposed for general systems of random variables (i.e. inconsistently connected systems). One such measure is based on quasi-couplings using negative probabilities (here denoted by [Formula: see text], Dzhafarov & Kujala, 2016 Quantum interaction). Dzhafarov & Kujala (Dzhafarov & Kujala 2019 Phil. Trans. R. Soc. A 377, 20190149. (doi:10.1098/rsta.2019.0149)) introduced a measure of contextuality, [Formula: see text], that naturally generalizes to a measure of non-contextuality. Dzhafarov & Kujala (Dzhafarov & Kujala 2019 Phil. Trans. R. Soc. A 377, 20190149. (doi:10.1098/rsta.2019.0149)) additionally conjectured that in the class of cyclic systems these two measures are proportional. Here we prove that conjecture is correct. Recently, Cervantes (Cervantes 2023 J. Math. Psychol. 112, 102726. (doi:10.1016/j.jmp.2022.102726)) showed the proportionality of [Formula: see text] and the Contextual Fraction measure introduced by Abramsky & Brandenburger (Abramsky & Brandenburger 2011 New J. Phys. 13, 113036. (doi:10.1088/1367-2630/13/11/113036)). The present proof completes the description of the interrelations of all contextuality measures proposed within or translated into the Contextuality-by-Default framework so far as they pertain to cyclic systems. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.

Quantum-like model for unconscious-conscious interaction and emotional coloring of perceptions and other conscious experiences

Quantum measurement theory is applied to quantum-like modeling of coherent generation of perceptions and emotions and generally for emotional coloring of conscious experiences. In quantum theory, a system should be separated from an observer. The brain performs self-measurements. To model them, we split the brain into two subsystems, unconsciousness and consciousness. They correspond to a system and an observer. The states of perceptions and emotions are described through the tensor product decomposition of the unconscious state space; similarly, there are two classes of observables, for conscious experiencing of perceptions and emotions, respectively. Emotional coloring is coupled to quantum contextuality: emotional observables determine contexts. Such contextualization reduces degeneration of unconscious states. The quantum-like approach should be distinguished from consideration of the genuine quantum physical processes in the brain (cf. Penrose and Hameroff). In our approach the brain is a macroscopic system which information processing can be described by the formalism of quantum theory. The paper is concluded with experimental test of contextual emotional coloring of conscious experiences based on Bell type inequalities which are treated in the contextual framework.