Abstract
We present an infrastructure for describing and handling uncertainty and vagueness in a combination of Description Logics and rules in the Semantic Web. More concretely, we apply fuzzy set theory to hybrid MKNF knowledge bases, and establish fuzzy hybrid MKNF knowledge bases, which is sound with respect to the classical two-valued semantics. Furthermore, we discuss some fundamental properties of fuzzy semantics, and characterize fuzzy MKNF models of general MKNF knowledge bases. We also provide characterizations of fuzzy MKNF models of positive and stratified MKNF knowledge bases in terms of a fixpoint operator and an iterative fixpoint semantics, respectively. Finally, we describe a special case of fuzzy nondisjunctive positive MKNF knowledge base, in which the truth value of a modal atom can be computed in polynomial time in the data complexity.