A Structure of Domain Ontologies and their Mathematical Models
Alexander Kleshchev, Irene Artemjeva · 2001
A primitive conceptualization is defined as the set of allintended situations. Anon–primitive conceptualization is defined as the set of all the pairs every of which consists ofan intended knowledge system and the set of all thesituations admitted by the knowledge system. The reality ofa domain is considered as the set of all the situation whichhave ever taken place in the past, are taking place nowand will take place in the future. A conceptualization isdefined as precise if the set of intended situations is equalto the domain reality. The representation of variouselements of a domain ontology in a model of the ontologyis considered. These elements are terms for situationdescription and situations themselves, terms for knowledgedescription and knowledge systems themselves,mathematical terms and constructions, auxiliary terms andontological agreements.It has been shown that any ontology representing a conceptualization has to be non–primitive if either (1) a conceptualization containsintended situations of different structures, or (2) aconceptualization contains concepts designated by termsfor knowledge description, or (3) a conceptualizationcontains concept classes and determines properties of theconcepts belonging to these classes, but the conceptsthemselves are introduced by domain knowledge, or (4)some restrictions on meanings of terms for situationdescription in a conceptualization depend on the meaningof terms for knowledge description.