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Abduction in Well-Founded Semantics and Generalized Stable Models via Tabled Dual Programs

By José Júlio Alferes, Luís Moniz Pereira and Terrance Swift

Abstract

Abductive logic programming oers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming oers a computational mechanism that provides a level of declarativity superior to 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. The result is the ability to compute abduction over well-founded semantics with explicit negation and answer sets. Our approach consists of a transformation and an evaluation method. The transformation adjoins to each objective literal O in a program, an objective literal not(O) along with rules that ensure that not(O) will be true if and only if O 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 on answer sets. Further, Abdual is asymptotically as ecient 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 publicly available meta-interpreter has been developed for Abdual using the XSB system

Topics: abduction, well-founded semantics, generalized
Publisher: Cambridge University Press
Year: 2004
OAI identifier: oai:CiteSeerX.psu:10.1.1.134.3580
Provided by: CiteSeerX
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