A decidable query answering algorithm for circumscriptive theories

Abstract

We describe a decidable algorithm to answer queries in circumscriptive theories, that allows the use of variable predicates. This significantly extends the results obtained in our earlier paper [P], where a similar algorithm was constructed for circumscriptive theories without variable predicates.Since prioritized circumscription is equivalent to a conjunction of parallel circumscriptions with variables, the algorithm can be used to answer queries in theories circumscribed by prioritized circumscription. The Closed-World Assumption (CWA) and its generalization, the Extended Closed-World Assumption (ECWA), can be considered as a special form of circumscription. Consequently, our method also applies to answering queries in theories using the Closed-World Assumption or its generalizations.For the sake of clarity, we restrict our attention to theories consisting of ground clauses. Our algorithm, however, has a natural extension to theories consisting of arbitrary clauses.