Quantum semantics of text perception

Abstract

The paper presents quantum model of subjective text perception based on binary cognitive distinctions corresponding to words of natural language. The result of perception is quantum cognitive state represented by vector in the qubit Hilbert space. Complex-valued structure of the quantum state space extends the standard vector-based approach to semantics, allowing to account for subjective dimension of human perception in which the result is constrained, but not fully predetermined by input information. In the case of two distinctions, the perception model generates a two-qubit state, entanglement of which quantifies semantic connection between the corresponding words. This two-distinction perception case is realized in the algorithm for detection and measurement of semantic connectivity between pairs of words. The algorithm is experimentally tested with positive results. The developed approach to cognitive modeling unifies neurophysiological, linguistic, and psychological descriptions in a mathematical and conceptual structure of quantum theory, extending horizons of machine intelligence.

Figure 1

Quantum scheme of neuro-cognitive modeling. Cognitive and physiological terminologies reflect quantum-theoretic concepts (bold) in parallel way. In quantum approach, a cognitive-behavioral system is considered as a black box in relation to a potential alternative 0/1. Department of the black box responsible for the resolution of this alternative is observable, delineated from the context analogous to the Heienberg’s cut between the system and the apparatus in quantum physics. Relative to the dichotomic alternative 0/1, potential outcomes of the experiment are encoded by superposition vector state $\left|\mathrm{\Psi }\right.〉$ (1). If the experiment is performed, the system transfers to one of the superposed potential outcomes according to probabilities $p_i$.

Figure 2

Text perception model: construction of the quantum cognitive state from the text substrate. Source document with sentences delimited by black squares (a) is perceived through binary distinctions expressed by concepts A and B. Presence of words associated with A and B (identified with neighboring sets, see Calculation of amplitudes) marked by red and blue (b) categorizes sentences to semantic subspaces defined by distinction states (Table 1). Number of sentences in each category defines absolute values of the amplitudes $|c_{\mathit{ij}}|=\sqrt{p_{\mathit{ij}}}$ in cognitive state $\left|\mathrm{\Psi }\right.〉$ (4). The model is finalized by supplementing the amplitudes with phase factors $e^{i{\varphi }_{\mathit{ij}}}$ representing subjective dimension of text perception (c).

Figure 3

Left: semantic connection between concepts website and promotion quantified by concurrence entanglement measure (10) versus expert estimation of how well text answers the question $<<$What is website promotion?$>>$ for 15 probe documents. Gray bars show range of concurrence values accessible by tuning of quantum phases ${\varphi }_{\mathit{ij}}$ in perception model of each document. Compared to the phase-randomized concurrence (gray circles), phase-tuned values (black dots) increase $R^2$ from 0.54 to 0.81. Top right: ranking of the probe documents by Google search for the query website promotion. Bottom right: classical correlation (11) and the LSA cosine distance between the same concepts (Methods). $R^2$ are determination coefficients. Horizontal axis, data and statistical error bars are common for all panels except three documents for which classical correlation is undefined. All data are given in Table 2.