Embedding Non-Ground Logic Programs into Autoepistemic Logic for Knowledge-Base Combination

Abstract

In the context of the Semantic Web, several approaches to the combination of ontologies, given in terms of theories of classical first-order logic, and rule bases have been proposed. They either cast rules into classical logic or limit the interaction between rules and ontologies. Autoepistemic logic (AEL) is an attractive formalism which allows to overcome these limitations, by serving as a uniform host language to embed ontologies and nonmonotonic logic programs into it. For the latter, so far only the propositional setting has been considered. In this paper, we present several embeddings of normal and disjunctive non-ground logic programs under the stable-model semantics into first-order AEL, and compare them in combination with classical theories, with respect to stable expansions and autoepistemic consequences. Our results reveal differences and correspondences of the embeddings and provide a useful guidance in the choice of a particular embedding for knowledge combination.