The SemanticWeb is an evolving extension of theWorld WideWeb in which the semantics of the available information are formally described, making it more machine-interpretable. The current W3C standard for Semantic Web ontology languages, OWL, is based on the knowledge representation formalism of Description Logics (DLs). Although standard DLs provide considerable expressive power, they cannot express various kinds of imprecise or vague knowledge and thus cannot deal with uncertainty, an intrinsic feature of the real world and our knowledge. To overcome this deficiency, this paper extends a standard Description Logic to a family of norm-parameterized Fuzzy Description Logics. The syntax to represent uncertain knowledge and the semantics to interpret fuzzy concept descriptions and knowledge bases are addressed in detail. The paper then focuses on a procedure for reasoning with knowledge bases in the proposed Fuzzy Description Logics. Finally, we prove the soundness, completeness, and termination of the reasoning procedure.
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