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Quantum Cognitive Triad: Semantic Geometry of Context Representation

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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.

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Notes

  1. Such coarse-graining of observables considered as a fundamental premise of quantum theory (Kofler and Brukner 2007) conforms with a discrete representation of information in the human’s brain (Tee and Taylor 2020).

  2. Cf. with the propensity interpretation of probability (Popper 1978a) and a tensed ontology of events described in Guarino (2017).

  3. While consensus on the nature of creativity and free will is not reached, quantum models of behavior have space for phenomena of this kind (Briegel 2012; Stapp 2017).

  4. Generally two different constants allowing for asymmetric composition of \(\left| \Psi _a\right\rangle\) and \(\left| \Psi _b\right\rangle\) in (6).

  5. In close analogy with an algorithm for sorting of contextual representations based on neural phase encoding (Ten Oever et al. 2020).

  6. The Bloch sphere thus can be considered as a visualization tool for subjective semantics of certainty and uncertainty (Hullman 2020).

  7. In the spirit of QBism (Fuchs et al. 2014; Khrennikov 2016; de Ronde et al. 2019).

  8. This triple is not to be confused with three truth values addressed by ternary logic (Toffano and Dubois 2020).

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Acknowledgements

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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Correspondence to Ilya A. Surov.

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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

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