Issues of Decidability for Description Logics in the Framework of Resolution

Abstract

We describe two methods on the basis of which effcient resolution decision procedures can be developed for a range of description logics. The first method uses an ordering restriction and applies to the description logic $\mathcal{A}\mathcal{L}\mathcal{B}$ , which extends $\mathcal{A}\mathcal{L}\mathcal{C}$ with the top role, full role negation, role intersection, role disjunction, role converse, domain restriction, range restriction, and role hierarchies. The second method is based solely on a selection restriction and applies to reducts of $\mathcal{A}\mathcal{L}\mathcal{B}$ without the top role and role negation. The latter method can be viewed as a polynomial simulation of familiar tableaux-based decision procedures. It can also be employed for automated model generation.