Reasoning with fuzzy extensions of OWL and OWL 2

Fuzzy Description Logics (f-DLs) have been proposed as logical formalisms capable of representing and reasoning with vague/fuzzy information. They are envisioned to be helpful for many applications that need to cope with such type of information such as multimedia processing, decision making, automatic negotiation and more. Recent results have provided with many tableaux algorithms for supporting reasoning over quite expressive f-DLs. However, no (direct) tableaux algorithm for reasoning with fuzzy extensions of DLs such as and exists today. and are particularly interesting formalisms as they constitute the logical underpinnings of the Web ontology languages OWL DL and OWL 2 DL. In the current paper, we present an algorithm for reasoning with the fuzzy DLs f- and f-. In addition, we also provide a tableaux algorithm for fuzzy nominals, thus providing reasoning support for the fuzzy DL language (we call) f-SHO(f)IQ.