Query Answering for OWL-DL with Rules

Abstract

Both OWL-DL and function-free Horn rules are decidable logics with interesting, yet orthogonal expressive power: from the rules perspective, OWL-DL is restricted to tree-like rules, but provides both existentially and universally quantified variables and full, monotonic negation. From the description logic perspective, rules are restricted to universal quantification, but allow for the interaction of variables in arbitrary ways. Clearly, a combination of OWL-DL and rules is desirable for building Semantic Web ontologies, and several such combinations have already been discussed. However, such a combination might easily lead to the undecidability of interesting reasoning problems. Here, we present a decidable such combination which is, to the best of our knowledge, more general than similar decidable combinations proposed so far. Decidability is obtained by restricting rules to so-called DL-safe ones, requiring each variable in a rule to occur in a non-DL-atom in the rule body. We show that query answering in such a combined logic is decidable, and we discuss its expressive power by means of a non-trivial example. Finally, we present an algorithm for query answering in $\mathcal{SHIQ}(\mathbf{D})$ extended with DL-safe rules based on the reduction to disjunctive datalog.