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.
Highlights
The article opens a series of publications on the linguistics of relations, the purpose of which is to formalize the processes studied by linguistics, to expand the possibilities of their use in artificial intelligence systems
Questions of categorization are presented in detail in cognitive linguistics
The research materials are presented in the form of mathematical proofs of various properties of the linguistic model associated with the process of categorization
Summary
This article opens a series of publications on the linguistics of relations (Rlinguistics) – a formal direction in linguistics. Formalization is the basis of any computer application of linguistics This series of articles aims to build the axiomatic foundations of the model of the world, formed by consciousness and underlying linguistic human activity. Categorization only by signs is fruitless: it describes the placement of objects in boxes with different names, and nothing more Another thing is when signs identify categories obtained for other reasons. In this case, observing the features of objects, one can make predictions of those processes that lie in the basis of one or another categorization. The research materials are presented in the form of mathematical proofs of various properties of the linguistic model associated with the process of categorization
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