f-DLPs: Extending Description Logic Programs with Fuzzy Sets and Fuzzy Logic

The Semantic Web can be viewed as largely about "Knowledge meets the Web". Thus its vision includes ontologies and rules. A key requirement for the architecture of the Semantic Web is to be able to layer "rules on top of ontologies" and "ontologies on top of rules". This has as a counterpart the definition of a mapping between Description Logics and Logic Programming, which is known as Description Logic Programs. In this paper we extend the Description Logic Programs with fuzzy sets and fuzzy logic in order to be able to represent the imprecision and vagueness of real-life applications. We provide the common semantics of the mapping, and the conditions that must be met for this semantic equivalence, based on the model-theoretic semantics.