TY - JOUR

T1 - Quantum cognition based on an ambiguous representation derived from a rough set approximation

AU - Gunji, Yukio Pegio

AU - Sonoda, Kohei

AU - Basios, Vasileios

N1 - Funding Information:
We acknowledge JSPS ( Japan Society for the Promotion of Science ) for funding our research ( 25280091 ).
Publisher Copyright:
© 2016.

PY - 2016/3/1

Y1 - 2016/3/1

N2 - Over the last years, in a series papers by Arecchi 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 judgment, basic cognitive process of decision making, as an inverse Bayes inference classifying the information content of neuron spike trains. It has been shown that for successive plural stimuli 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 an ambiguous representation by an observer within a universe of discourse. In our work the ambiguous representation of an object or a stimuli is defined as 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 approximations, correspondingly, for the initial data sets that are derived with respect to each map. Upper and lower approximations herein are defined in the context of "rough set" analysis. The inverse Bayes inference is implemented by the lower approximations with respect to the one map and for the upper approximation with respect to the other map for a given data set. 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.

AB - Over the last years, in a series papers by Arecchi 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 judgment, basic cognitive process of decision making, as an inverse Bayes inference classifying the information content of neuron spike trains. It has been shown that for successive plural stimuli 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 an ambiguous representation by an observer within a universe of discourse. In our work the ambiguous representation of an object or a stimuli is defined as 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 approximations, correspondingly, for the initial data sets that are derived with respect to each map. Upper and lower approximations herein are defined in the context of "rough set" analysis. The inverse Bayes inference is implemented by the lower approximations with respect to the one map and for the upper approximation with respect to the other map for a given data set. 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.

KW - Bayes inference

KW - Cognition

KW - Inverse Bayes inference

KW - Ortho-modular lattice

KW - Quantum logic

UR - http://www.scopus.com/inward/record.url?scp=84959420379&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959420379&partnerID=8YFLogxK

U2 - 10.1016/j.biosystems.2015.12.003

DO - 10.1016/j.biosystems.2015.12.003

M3 - Article

C2 - 26861118

AN - SCOPUS:84959420379

SN - 0303-2647

VL - 141

SP - 55

EP - 66

JO - BioSystems

JF - BioSystems

ER -