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Over the last years, in a series papers by Arrechi and others, a model forthe cognitive processes involved in decision making has been proposed andinvestigated. The key element of this model is the expression of apprehensionand judgement, basic cognitive process of decision making, as an inverse Bayesinference classifying the information content of neuron spike trains. Forsuccessive plural stimuli, it has been shown that this inference, equipped withbasic non-algorithmic jumps, is affected by quantum-like characteristics. Weshow here that such a decision making process is related consistently withambiguous representation by an observer within a universe of discourse. In ourwork ambiguous representation of an object or a stimuli is defined by a pair ofmaps from objects of a set to their representations, where these two maps areinterrelated in a particular structure. The a priori and a posteriorihypotheses in Bayes inference are replaced by the upper and lowerapproximation, correspondingly, for the initial data sets each derived withrespect to a map. We show further that due to the particular structuralrelation between the two maps, the logical structure of such combinedapproximations can only be expressed as an orthomodular lattice and thereforecan be represented by a quantum rather than a Boolean logic. To our knowledge,this is the first investigation aiming to reveal the concrete logic structureof inverse Bayes inference in cognitive processes.

Quantum Cognition based on an Ambiguous Representation Derived from a Rough Set Approximation