A Query Evaluation Method for Abductive Logic Programming Based on Generalized Stable Models

Abstract

Abduction has been recognized as important human reasoning and has been applied in various fields (See for example[Eshghi 89]). It is also related with logic programming, especially with negation as failure [Eshghi 89, Kakas 90a, Kakas 90b]. Eshghi and Kowalski [Eshghi 89] introduce abduction to handle negation as failure and Kakas and Mancarella [Kakas 90a, Kakas 90b] extend [Eshghi 89] to include any arbitrary abducible predicate. We have already proposed a correct bottom-up procedure to compute abduction [Satoh 91]. This procedure computes generalized stable models [Kakas 90a] for computing abduction. However, this procedure is not suitable for a query evaluation. Although [Kakas 90b] proposes a query evaluation method by extending the procedure in [Eshghi 89], there is a problem of incorrectness in the procedure in [Eshghi 89] and the problem is inherited to the procedure in [Kakas 90b]. Moreover, their procedures can only handle a limited class of integrity constraints. Our proposed procedure in this paper is correct for any consistent abductive framework proposed in [Kakas 90a]. In other words, if the procedure succeeds, there is a set of hypotheses which satisfies a query, and if the procedure finitely fails, there is no such set. We can guarantee the above correctness since we adopt a forward evaluation of rules and check consistency of "implicit deletion" [Sadri 88]. Thanks to the forward evaluation of rules, we can also handle any form of integrity constraints.