Mathematical Models of Domain Ontologies

* This paper was made according to the program No 14 of fundamental scientific research of the Presidium of the Russian Academy of Sciences, the project "Intellectual Systems Based on Multilevel Domain Models".

In this article the notion of a mathematical model of domain ontology is introduced. The mathematical apparatus (unenriched logical relationship systems) is essentially used. The representation of various elements of domain ontology in its model is considered. These elements are terms for situation description and situations themselves, knowledge and terms for knowledge description, mathematical terms and constructions, auxiliary terms and ontological agreements. The notion of a domain model is discussed. The notions of a precise ontology and precise conceptualization are introduced. The structures of situations and knowledge and also their properties are considered. Merits and demerits of various classes of the domain ontology models are discussed.