Abstract

The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms, into a framework that is more useful for describing semantic content. In particular, combining logic programming with the Web Ontology Language (OWL), which is a standard based on description logics, emerged as an important issue for linking the Rules and Ontology Layers of the Semantic Web. Non-monotonic description logic programs (or dl-programs) were introduced for such a combination, in which a pair (L,P) of a description logic knowledge base L and a set of rules P with negation as failure is given a model-based semantics that generalizes the answer set semantics of logic programs. In this paper, we reconsider dl-programs and present a well-founded semantics for them as an analog for the other main semantics of logic programs. It generalizes the canonical definition of the well-founded semantics based on unfounded sets, and, as we show, lifts many of the well-known properties from ordinary logic programs to dl-programs. Among these properties: our semantics amounts to a partial model approximating the answer set semantics, which yields for positive and stratified dl-programs a total model coinciding with the answer set semantics; it has polynomial data complexity provided the access to the description logic

Citations