Prime Implicate Normal Form for ALC Concepts

In this paper, we present a new normal form for concept expressions in the description logic ALC which is based on a recently introduced notion of prime implicate. We show that concepts in prime implicate normal form enjoy a number of desirable properties which make prime implicate normal form interesting from the viewpoint of knowledge compilation. In particular, we prove that subsumption between ALC concepts in prime implicate normal form can be carried out in polynomial time using a simple structural subsumption algorithm reminiscent of those used for less expressive description logics. We provide a sound and complete algorithm for putting concepts into prime implicate normal form, and we investigate the spatial complexity of this transformation, showing there to be an at most doubly-exponential blowup in concept size. At the end of the paper, we compare prime implicate normal form to two other normal forms for ALC that have been proposed in the literature, discussing the relative merits of the different approaches. Proofs of all results can be found in an accompanying technical report [1].