Abduction in Well-Founded Semantics and Generalized Stable Models

TL;DR

This paper presents a novel approach using tabled logic programming to evaluate abductive frameworks with well-founded semantics and explicit negation, enabling efficient computation of abduction and query evaluation.

Contribution

It introduces a transformation and an evaluation method, extsf{wfsmeth}, for abductive reasoning with explicit negation within well-founded semantics using tabled logic programming.

Findings

extsf{wfsmeth} is sound and complete for abductive frameworks with well-founded semantics.

The method is asymptotically as efficient as existing methods for similar problems.

A meta-interpreter implementation is available in the XSB system.

Abstract

Abductive logic programming offers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming offers a computational mechanism that provides a level of declarativity superior to that of Prolog, and which has supported successful applications in fields 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 {\em dual} program. The evaluation method, \wfsmeth, then operates on the dual program. \wfsmeth{} 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, \wfsmeth{} is asymptotically as efficient as any known method for either class of problems. In addition, when abduction is not desired, \wfsmeth{} 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 \wfsmeth{} using the XSB system.