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It is constructed by enhancing the idea of active inference and/or embodied intelligence. Excess Bayesian inference is implemented by extending the key idea of Bayesian inference beyond classic Bayesian inference and its variations. In this work, we introduce “excess Bayesian inference” and show that this excess Bayesian inference entails an underlying orthomodular lattice, while classic Bayesian inference entails a Boolean lattice. Thus, we address this challenging issue to bridge and connect the free energy minimization principle with the theory of quantum cognition. While free energy minimization, which incorporates Bayesian inference, leads to a Boolean lattice of propositions (classical logic), quantum cognition, which seems to be very dissimilar to Bayesian inference, leads to an orthomodular lattice of propositions (quantum logic). It appears that the free energy minimization principle conflicts with quantum cognition since the former adheres to a restricted view based on experience while the latter allows deviations from such a restricted view. 3Service de Physique des Systèmes Complexes et Mécanique Statistique and Interdisciplinary Center for Nonlinear Phenomena and Complex Systems (C.P.231 CeNoLi-ULB), Université Libre de Bruxelles, Brussels, Belgium.