Fuzzy extensions of OWL: Logical properties and reduction to fuzzy description logics

The Semantic Web is an extension of the current web, where information would have precisely defined meaning, based on formal semantics, and structured using a knowledge representational language. The current W3C standard for representing knowledge is the Web Ontology Language (OWL). OWL is based on Description Logics which is a popular knowledge representation formalism. Although, DLs are quire expressive they feature limitations with respect to what can be said about vague knowledge, which appears in several applications. Consequently, fuzzy extensions to OWL and DLs have gained considerable attention. In the current paper we study fuzzy extensions of the semantic web language OWL. First, we present the (abstract) syntax and semantics of a simplistic fuzzy extension of OWL creating fuzzy OWL (f-OWL). More importantly we use this extension to provide an investigation on the semantics of several f-OWL axioms and more precisely for those which can be expressed in many different ways (at least in classical DLs) and analyze their intuitive meaning. Moreover, we present a translation method which reduces inference problems of f-OWL into inference problems of expressive fuzzy Description Logics, in order to provide reasoning support through (fuzzy) DLs. Finally, we provide two further fuzzy extensions of OWL based on fuzzy subsumptions and fuzzy nominals.