Exact Reasoning over Imprecise Ontologies

A real world of objects (individuals) is represented by a set of assertions written with respect to defined syntax and semantics of description logic (formal language). These assertions should be consistent with the ontology axioms described as terminology of knowledge. The axioms and the assertions represent ontology about a particular domain. A real world is a possible world if all the assertions and the axioms over its set of individuals, are consistent. It is possible then to query the possible world by specific assertions (as instance checking) to determine if they are consistent with it or not. However, ontology can contain vague concepts which means the knowledge about them is imprecise and then query answering will not possible due to the open world assumption if the necessary information is incomplete (it is currently absent). A concept description can be very exact (crisp concept) or exact (fuzzy concept) if its knowledge is complete, otherwise it is inexact (vague concept) if its knowledge is incomplete. In this paper we propose a vagueness theory based on the definition of truth gaps as ontology assertions to express the vague concepts in Ontology Web Language (OWL2) (which is based on the description logic SROIQ(D)) and an extension of the Tableau algorithm for reasoning over imprecise ontologies.