Well-founded Abduction via Tabled Dual Programs

Abductive Logic Programming ooers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled Logic Programming ooers a computational mechanism that provides a level of declarativity above that of Prolog, and which has supported successful applications in elds such as parsing, program analysis, and model checking. In this paper we show how to use tabled logic programming to evaluate queries to abductive frameworks with integrity constraints when these frameworks contain both default and explicit negation. Our approach consists of a transformation and an evaluation method. The transformation adjoins to each rule R of a nite ground program a new rule that is true if and only if R is false. We call the resulting program a dual program. The evaluation method, Abdual, then operates on the dual program. Abdual is sound and complete for evaluating queries to abductive frameworks whose entailment method is based on either the well-founded semantics with explicit negation, or answer sets. Further, Abdual is asymptotically as eecient as any known method for either class of problems. In addition, when abduction is not desired, Abdual operating on a dual program provides a novel tabling method for evaluating queries to ground extended programs whose complexity and termination properties are similar to those of the best tabling methods for the well-founded semantics. A publically available meta-interpreter has been developed for Abdual using the XSB system.