Institution: Oxford University
Description Logics are knowledge representation formalisms that provide, for example, the logical underpinning of the W3C standards OWL Lite and OWL DL, and the upcoming standard OWL 2. Conjunctive queries, the standard query language in databases, have recently gained significant attention as an expressive query language for Description Logic knowledge bases. Several different techniques for deciding conjunctive query entailment are available for a wide range of DLs. Nevertheless, only for the DL that underpins OWL Lite, decidability of conjunctive query entailment is known. So far, the combination of nominals, inverse roles, and number restrictions in OWL DL and OWL 2 caused unsolvable problems for the available techniques. We tackle this problem and present a decidability result for entailment of unions of conjunctive queries in the DL ALCHOIQb that contains the all three problematic constructors simultaneously. Provided that queries contain only simple roles, our result also shows decidability of entailment of (unions of) conjunctive queries in the logic that underpins OWL DL and we believe that the presented results will pave the way for further progress towards conjunctive query entailment decision procedures for the Description Logics underlying the OWL standards.