Dealing with Inconsistency When Combining Ontologies and Rules Using DL-Programs

Description Logic Programs (DL-programs) have been introduced to combine ontological and rule-based reasoning in the context of the Semantic Web. A DL-program loosely combines a Description Logic (DL) ontology with a non-monotonic logic program (LP) such that dedicated atoms in the LP, called DL-atoms, allow for a bidirectional flow of knowledge between the two components. Unfortunately, the information sent from the LP-part to the DL-part might cause cut inconsistency in the latter, leading to the trivial satisfaction of every query. As a consequence, in such a case, the answer sets that define the semantics of the DL-program may contain spoiled information influencing the overall deduction. For avoiding unintuitive answer sets, we introduce a refined semantics for DL-programs that is sensitive for inconsistency caused by the combination of DL and LP, and dynamically deactivates rules whenever such an inconsistency would arise. We analyze the complexity of tin new semantics, discuss implementational issues and introduce a notion of stratification that guarantees uniqueness of answer sets,