Dempster-Shafer logical model for fuzzy Description Logics

Description Logics, defined as a family of knowledge representation languages, have gained a lot of popularity, due to their connection with the Semantic Web, and more precisely, with the Web Ontology Language - OWL (OWL-DL). Vague information cannot be considered negligible when dealing with Semantic Web tasks. In this context, the definition of fuzzy DLs has been emerged. The Semantics of any DL is defined by an interpretation, which can be considered as a state of a world, where a DL formula (crisp or fuzzy) holds. In our method, we consider an uncertainty extension in a fuzzy DL, in the sense that an axiom holds with a belief degree. In order to represent these axioms, we assume Dempster-Shafer basic probability assignments on states of world (interpretations). We define the concept of Dempster-Shafer Fuzzy interpretation, in order to define semantics for our DL.