Combining Rules and Ontologies into Clopen Knowledge Bases

We propose Clopen Knowledge Bases (CKBs) as a new formalism combining Answer Set Programming (ASP) with ontology languages based on first-order logic. CKBs generalize the prominent r-hybrid and DL+LOG languages of Rosati, and are more flexible for specification of problems that combine open-world and closed-world reasoning. We argue that the guarded negation fragment of first-order logic (GNFO)—a very expressive fragment that subsumes many prominent ontology languages like Description Logics (DLs) and the guarded fragment—is an ontology language that can be used in CKBs while enjoying decidability for basic reasoning problems. We further show how CKBs can be used with expressive DLs of the ALC family, and obtain worst-case optimal complexity results in this setting. For DL-based CKBs, we define a fragment called separable CKBs (which still strictly subsumes r-hybrid and DL+LOG knowledge bases), and show that they can be rather efficiently translated into standard ASP programs. This approach allows us to perform basic inference from separable CKBs by reusing existing efficient ASP solvers. We have implemented the approach for separable CKBs containing ontologies in the DL ALCH, and present in this paper some promising empirical results for real-life data. They show that our approach provides a dramatic improvement over a naive implementation based on a translation of such CKBs into dl-programs.