A Mathematical Apparatus for Domain Ontology Simulation. An Extendable Language of Applied Logic

Abstract

A mathematical apparatus for domain ontology simulation will be described in the series of the articles. This article is the first one of the series. The paper is devoted to means for representation of domain models and domain ontology models, so here a logical language is used only as a means for formalizing ideas. The chief requirement to such a language is that it must have such a semantic basis that would allow us to determine the most exact approximation of a set of intended interpretation functions as often as possible. Another requirement closely connected with the foregoing one is that the awkwardness of expressing ideas in such a language must not considerably exceed the complexity of their expressing in natural language. There are two ways to meet the requirements. The first one is to define and fix a wide semantic basis of the language. In this case the semantic basis nonetheless can be insufficient for some applications of the language. Extending applications of the language can lead from time to time to the necessity of further extending its semantic basis, i.e. to the necessity of defining new and new versions of the language. The second way is to make the kernel of the language being as nearer to the semantic basis of the classical language as possible and to allow us to make necessary extensions of the kernel for particular applications. In this article the second way is used to define the extendable language of applied logic. The goal of this article is to define the kernel of the extendable language of applied logic and its standard extension. The standard extension of the language defines elements of the semantic basis that are supposed to be useful practically in all the applications.