Abstract
The paper describes an algorithm for semantic representation of behavioral contexts relative to a dichotomic decision alternative. The contexts are represented as quantum qubit states in two-dimensional Hilbert space visualized as points on the Bloch sphere. The azimuthal coordinate of this sphere functions as a one-dimensional semantic space in which the contexts are accommodated according to their subjective relevance to the considered uncertainty. The contexts are processed in triples defined by knowledge of a subject about a binary situational factor. The obtained triads of context representations function as stable cognitive structure at the same time allowing a subject to model probabilistically-variative behavior. The developed algorithm illustrates an approach for quantitative subjectively-semantic modeling of behavior based on conceptual and mathematical apparatus of quantum theory.
Notes
Generally two different constants allowing for asymmetric composition of \(\left| \Psi _a\right\rangle\) and \(\left| \Psi _b\right\rangle\) in (6).
In close analogy with an algorithm for sorting of contextual representations based on neural phase encoding (Ten Oever et al. 2020).
The Bloch sphere thus can be considered as a visualization tool for subjective semantics of certainty and uncertainty (Hullman 2020).
This triple is not to be confused with three truth values addressed by ternary logic (Toffano and Dubois 2020).
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I thank I.A. Sazanovich for help in the preparation of the text and three anonymous reviewers for their comments and advice.
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Surov, I.A. Quantum Cognitive Triad: Semantic Geometry of Context Representation. Found Sci 26, 947–975 (2021). https://doi.org/10.1007/s10699-020-09712-x
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DOI: https://doi.org/10.1007/s10699-020-09712-x