Reasoning with Vague Concepts in Description Logics

The open world assumption in ontologies representing knowledge may assign deficient (imprecise) meaning for ontology concepts which are language adjectives referring the meaning of classes of objects (individuals). The interpretation of an imprecise (vague) concept is by three subsets of individuals. The first subset of individuals surely belongs to the vague concept, the second subset of individuals surely doesn't belong the vague concept and the third subset is in the borderline. In this paper, the authors will show that is possible to describe ontology vague concepts using well-defined formal languages. The authors will propose also an extension of the Tableau algorithm for reasoning over vague ontologies.