Querying OWL 2 QL and Non-monotonic Rules

Answering (conjunctive) queries is an important reasoning task in Description Logics (DL), hence also in highly expressive ontology languages, such as OWL. Extending such ontology languages with rules, such as those expressible in RIF-Core, and further with non-monotonic rules, integrating default negation as described in the RIF-FLD, yields an even more expressive language that allows for modeling defaults, exceptions, and integrity constraints. Here, we present a top-down procedure for querying knowledge bases (KB) that combine non-monotonic rules with an ontology in DL-LiteR – the DL underlying the OWL 2 profile OWL 2 QL. This profile aims particularly at answering queries in an efficient way for KB with large ABoxes. Our procedure extends the query-answering facility to KB that also include non-monotonic rules, while maintaining tractability of reasoning (w.r.t. data complexity). We show that the answers are sound and complete w.r.t. the well-founded MKNF model for hybrid MKNF KB K.