Quantum Cognitive Triad: Semantic Geometry of Context Representation

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.

Quantum core affect. Color-emotion structure of semantic atom

“…Unlike standard Euclidean geometry, orthogonality of the qubit states corresponds to the opposite orientation, as seen for basis vectors 0|1 = 0, pointing to the poles of the sphere. By representing context in relation to the basis decision to be made, the qubit state (Equation 1) encodes its meaning in subjective experience of the considered person (Surov, 2022).…”

“…2). While maintaining key features of the quantum approach such as contextuality, superposition, and entanglement, it is unique in allowing simple geometrical representation, recently interpreted as an individual semantic space (Surov, 2021). Furthermore, the qubit structure is shown to encode elementary states of emotional experience (Surov, 2022).…”

“…While maintaining key features of the quantum approach such as contextuality, superposition, and entanglement, it is unique in allowing simple geometrical representation, recently interpreted as an individual semantic space (Surov, 2021). Furthermore, the qubit structure is shown to encode elementary states of emotional experience (Surov, 2022). This link allows mapping of color to qubit states both mathematically and semantically, providing complete psychological interpretation for this particular class of quantum-cognitive states.…”

“…This result is approached in the following steps. First, Section 2 outlines the quantum-theoretic model of semantic space (Surov, 2022), central to the following analysis. Next, Section 3 summarizes previously established meanings of basic colors, including state of the art in color-emotion correspondence and relevant models of color.…”

Quantum Structure in Human Perception

“…The identification of the presence of quantum structures in human cognition, and its importance for the development of performant quantum structure-based models for bounded rationality situations and human decisions, led to a field of research now called 'quantum cognition' (Aerts & Aerts, 1995;Gabora & Aerts, 2002;Bruza & Cole, 2005;Aerts & Gabora, 2005a,b;Busemeyer et al, 2006;Bruza & Gabora, 2009;Aerts, 2009a,b;Aerts & Sozzo, 2011;Aerts et al, 2012;Busemeyer & Bruza, 2012;Haven & Khrennikov, 2013;Dalla Chiara et al, 2015;Pothos et al, 2015;Blutner & beim Graben, 2016;Moreira & Wichert, 2016;Gabora & Kitto, 2017;Surov, 2021;Pothos & Busemeyer, 2022). Parallel to the emergence of the research field of quantum cognition, quantum structures were identified in computer science, their use especially in information retrieval and natural language processing leading to important results, and also bringing a new research domain to life called 'quantum information science' (Aerts & Czachor, 2004;Van Rijsbergen, 2004;Widdows, 2004;Song et al, 2010;Melucci, 2015;Aerts et al, 2019).…”