Interval rough mereology and description logic: An approach to formal treatment of imprecision in the Semantic Web ontologies

Learning and maintaining ontologies play critically important roles in the Semantic Web. Ontologies provide formal and explicit semantics to available knowledge and make possible shared understanding of a domain. A great deal of knowledge in the Semantic Web involves different sorts of imprecision. Common examples of imprecise knowledge include various statistical hypotheses, vagueness and ambiguities of natural language and many others. Consequently, ontologies must be expressive enough to handle imprecision. This paper presents an approach to formal handling of granularity as a special kind of imprecision in ontologies. It is based on Soft Computing techniques, in particular, Rough Set and Fuzzy Set theories. The approach also makes heavy use of Rough Mereology - a recently proposed paradigm for approximate reasoning - to compute degrees of imprecision of ontological concepts, relationships and assertions. It is demonstrated how the proposed mereological approach can be used together with the framework for representing uncertainty in Description Logic - family of popular logics for specifying formal ontologies. Finally, the paper introduces interval computations to the area of representing and reasoning with ontologies and shows how intervals can formally capture the imprecision incurred by computing rough inclusion (mereological) functions.