Embedding Approaches to Combining Rules and Ontologies into Autoepistemic Logic

The combination of rules and ontologies has a central role in the ongoing development of the Semantic Web. In previous work, autoepistemic logic (AEL) was advocated as a uniform host formalism to study different such combinations, enabling comparisons on a common basis. In this paper, we continue this line of research and investigate different embeddings of major proposals to combine rules and ontologies into first-order autoepistemic logic (FO-AEL). In particular, we present embeddings for dl-programs, r-hybrid knowledge bases, and hybrid MKNF knowledge bases, which are representatives of different combination types. We study the embeddings in the context of FO-AEL under the standard-names assumption, but we also discuss variants using the anyand all-names semantics. Our results provide interesting insights into the properties of the discussed combination formalisms.