Formal Analysis Of Domain-Specific Ontologies

Ontology is one of the branches of Philosophy. It is the theory which deals with the nature and essence of being. Recently, the research about Ontology is developed widely in computer science. It will be advantageous to manage the information of a domain, if we construct a domain-specific ontology by abstracting or generalizing this domain to a set of concepts and their inter-relations. With ontological methods being used widely, research about mathematization of ontologies has been developed deeply. In this thesis, we adopt methods of Formal Concept Analysis and set up a mathematical model for domain-specific ontologies.In Formal Concept Analysis, a concept is formalized to a pair of sets, a set of objects and a set of attributes, which are corresponding each other. These two sets denote the extension and intension of a formal concept respectively. And the mapping (?' is defined to reflect the determining and corresponding relations between these two sets. In ontologies, intensions of categories are denned by attributes andrelations. Hence, at first, we give the definition of a structure-frames, whichis proper for the representation of intensions of categories. Also, we analyze the properties of this structure detailedly. Then we study the categories in ontologies by means of Formal Concept Analysis. At last, we prove the equivalence of relations of categories, their intensions and extensions in the three separate partial order sets.