Abstract

Introduction. The article opens a series of publications on the linguistics of relations (hereinafter R–linguistics), the purpose of which is to formalize the processes studied by linguistics, to expand the possibilities of their use in artificial intelligence systems. At the heart of R-linguistics is the hypothesis that mental and linguistic activity is based on the use of consciousness model of the world, which is a system of specially processed relationships observed in the world or received by consciousness in the process of communication.Methodology and sources. This article is devoted to the axiomatization of the categorization process. The research methods consist of the development of necessary mathematical concepts for linguistics.Results and discussion. Axioms of categorization are defined and their equivalence with other systems of axioms is established. The concept of linguistic spaces, which consist of categories formed on the basis of axioms, is formulated. The properties of linguistic spaces are defined. In the paper are introduced the concepts of forming species which are important in decompositions of spaces, and in the transition to a parametric representation and language. Three variants of categorization are considered, the most important of which is verbal categorization. The evaluation of the results and their further development in different directions is carried out.Conclusion. At the end of the article some additional comments are made for further publications of the series.