Over the last years, in a series papers by Arrechi and others, a model for
the cognitive processes involved in decision making has been proposed and
investigated. The key element of this model is the expression of apprehension
and judgement, basic cognitive process of decision making, as an inverse Bayes
inference classifying the information content of neuron spike trains. For
successive plural stimuli, it has been shown that this inference, equipped with
basic non-algorithmic jumps, is affected by quantum-like characteristics. We
show here that such a decision making process is related consistently with
ambiguous representation by an observer within a universe of discourse. In our
work ambiguous representation of an object or a stimuli is defined by a pair of
maps from objects of a set to their representations, where these two maps are
interrelated in a particular structure. The a priori and a posteriori
hypotheses in Bayes inference are replaced by the upper and lower
approximation, correspondingly, for the initial data sets each derived with
respect to a map. We show further that due to the particular structural
relation between the two maps, the logical structure of such combined
approximations can only be expressed as an orthomodular lattice and therefore
can be represented by a quantum rather than a Boolean logic. To our knowledge,
this is the first investigation aiming to reveal the concrete logic structure
of inverse Bayes inference in cognitive processes.Comment: 23 pages, 8 figures, original research pape