R-linguistics. The Principle of Linguistic Duality

Introduction. R-linguistics uses the axiomatic method in its approach to modeling the world and language [1]. Axioms define the categories of language, their properties and ways of formation. On this basis, when processing the accumulated data in the form of relations, it is possible to form systems of categories and determine the verbs connecting these categories. A reasonable question arises: if categories (to be such) must satisfy certain axioms, does this requirement apply to verbs as well? The purpose of this article is to deal with this issue.Methodology and sources. The results of the previous parts of the series are used as research tools. The axioms and methods of verb categorization formulated earlier are used to develop the necessary mathematical representations of the verb axiomatics.Results and discussion. The article introduces the axiom for the verbs of the language (the axiom of the verbal cross) and shows that this axiom is related to the categorization axiom (the correctness axiom). Although this connection is not identical, it becomes such with the additional use of the axiom of extensiveness. This relationship made it possible to formulate the fundamental principle of linguistics – the principle of duality.Conclusion. The axiomatics of verbs and categories of a language turns out to be connected, and one determines the other, so that by and large it does not matter which of them is the source of the model of the world and the appearance of language. This unity is formulated as the principle of duality in linguistics. The manifestations of the principle of duality in the language are diverse, but this article focuses on the discussion of the appearance in the language of verbs-processes and adverbs. This transition is considered, starting with obtaining the initial data about the world, to the emergence of ideas about processes and adverbs as a feature system of verbs.