Combining First-order Logic and Logic Programming Using Fol-programs

The integration of knowledge bases in classical first-order logic (and in particular of ontologies in various description logics) with rule languages rooted in logic programming is receiving considerable attention in the context of current efforts around Semantic-Web languages. Towards this integration we introduce fol-programs, which combine logic programs under the answer set and the wellfounded semantics with first-order logic knowledge bases and which generalize dl-programs, a closely related approach combining description logics with rules. Therefore, we define a syntax and a semantics for fol-programs, namely we define minimal model, strong answer set, weak answer set and well-founded semantics for fol-programs, to properly generalize the semantics of ordinary logic programs to fol-programs. We then show computational properties of fol-programs and prove that fol-programs are more expressive than dl-programs. Finally, we present our implementation of the well-founded semantics of fol-programs based on the deductive database engine Ontobroker and the automated theorem prover for first-order logic Vampire and discuss representative reasoning experiments on it.