Semantic Space: between Continuity and Infinity

Abstract

The paper describes approaches to unified knowledge representation, providing the formation of semantic space models. On the basis of previously proposed models for the representation of non-numeric structures with denotational and operational semantics, quantitative attributes and approaches to their calculation are proposed. They allow to reveal additional topological and metric properties of semantic space structures. A model of multiversal (protomultiversal) numbers is proposed. This model is a formal basis for clarifying the meaning and revealing semantic properties of network structures and models such as artificial neural networks, Kolmogorov-Arnold networks and other models with operational semantics and using numerical features to solve problems within the semantic space.