Fuzzy description logics and the semantic Web

In the last decade a substantial amount of work has been carried out in the context of Description Logics (DLs). DLs are a logical reconstruction of the so-called frame-based knowledge representation languages, with the aim of providing a simple well-established Tarski-style declarative semantics to capture the meaning of the most popular features of structured representation of knowledge. Nowadays, DLs have gained even more popularity due to their application in the context of the Semantic Web. Ontologies play a key role in the Semantic Web and major effort has been put by the Semantic Web community into this issue. Informally, an ontology consists of a hierarchical description of important concepts in a particular domain, along with the description of the properties (of the instances) of each concept. DLs play a particular role in this context as they are essentially the theoretical counterpart of the Web Ontology Language OWL DL, the state of the art language to specify ontologies. Web content is then annotated by relying on the concepts defined in a specific domain ontology. However, OWL DL becomes less suitable in all those domains in which the concepts to be represented have not a precise definition (which on the Web is likely the rule rather than an exception). We present the current state of the art of fuzzy description logics and present open issues to be addressed to make them appealing for the Semantic Web.