Connecting the free energy principle with quantum cognition - Gunji, Yukio-Pegio; Shinohara, Shuji; Basios, Vasileios (Frontiers in Neurorobotics, 2022)
It appears that the free energy minimization principle conflicts with quantum cognition, since the former sticks to a restricted view based on experience while the latter allows deviations from such a restricted view. While free energy minimization, which incorporates Bayesian inference, leads to a Boolean lattice of propositions (classical logic), quantum cognition which seems to be far from Bayesian inference, leads to an orthomodular lattice of propositions (quantum logic). Thus, we address this challenging issue in order to bridge and connect the free energy minimization principle with the theory of quantum cognition. In this work we introduce the ‘excess Bayesian inference’, and show that this excess Bayesian inference entails an underlying orthomodular lattice while classic Bayesian inference entails a Boolean lattice. Excess Bayesian inference is implemented by extending the key idea of Bayesian inference further and beyond than of the classic Bayesian inference and its variations. It is constructed by enhancing the idea of active inference and/or embodied intelligence. The appropriate lattice structure of its logic is obtained from a binary relation transformed from a distribution of joint probabilities of data and hypotheses, by employing a rough-set lattice technique in accordance to quantum cognition logic.