Abstract: 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.

Keywords: Domain ontology, domain ontology model, ontology language specification, kernel of extendable language of applied logic, unenriched logical relationship systems, enriched logical relationship systems, enrichment of logical relationship system.

ACM Classification Keywords: I.2.4 Knowledge Representation Formalisms and Methods, F.4.1. Mathematical Logic

Link:

MATHEMATICAL MODELS OF DOMAIN ONTOLOGIES1

Alexander Kleshchev, Irene Artemjeva

http://www.foibg.com/ijita/vol14/ijita14-1-p05.pdf