Tensor Representation of Semantic Space
Aleksandr Pliushch
The article addresses the limitations of classical vector models of semantic space, which neglect reflexivity, anticipation, and the subject’s self-development. Meaning is conceptualized as reflexive “knowledge about knowledge,” requiring continuous assessment of its subjective significance in evolving life situations. Grounded in post-non-classical methodology, the semantic space of a self-developing subject—integrating existing and prospective knowledge—functions simultaneously as the instrument, result, and process of semiosis, ensuring the inseparable coupling of knowledge and meaning within a unified cognitive structure. Tensor formalization relies on three mathematical characteristics: dimensionality, rank, and the transformation law. In cognitive terms, dimensionality defines the instrument’s “resolution capacity,” rank determines the number of the researcher’s reflexive positions, and the transformation law operates as an active cognitive operator that integrates multiple descriptions and positions into a single act of understanding. This act realizes the dialectical unity of content, context, and communication. In the proposed model, semantic space, serving as an instrument, is structured not as a point continuum but as an accumulated network of three-dimensional discrete cells that encode rules for meaning actualization based on the instrument’s pre-givenness, the author’s position, and the future application of the result. As an anticipated outcome, it is modeled as a rank-3 tensor specifying three subject-positions: actualized, constructed, and future-continuing. As a process, semantic space unfolds through the cyclic reduction of the tensor network’s potential states, generating new topologies and driving the co-evolution of instrument, author, and meaning. The tensor organization of the semantic space enables meaning to be conceptualized as a dynamic activation pattern within the network, where it is distributed, context-dependent, and evolves over time. The self-developing subject serves as the topological locus of self-reference, leveraging fractal recursion to increase mental organizational complexity. Ultimately, the approach endows semiosis with existential significance, transforming semantic space into an instrument for future-building and continuous self-development, thereby enabling the establishment of dynamic orientations under uncertainty.