Noboru Iwayama

Computing abduction by using TMS with top-down expectation

Abstract We present a method to compute abduction in logic programming. We translate an abductive framework into a normal logic program with integrity constraints and show the correspondence between generalized stable models and stable models for the translation of the abductive framework. Abductive explanations for an observation can be found from the stable models for the translated program by adding a special kind of integrity constraint for the observation. Then, we show a bottom-up procedure to compute stable models for a normal logic program with integrity constraints. The proposed procedure excludes the unnecessary construction of stable models on early stages of the procedure by checking integrity constraints during the construction and by deriving some facts from integrity constraints. Although a bottom-up procedure has the disadvantage of constructing stable models not related to an observation for computing abductive explanations in general, our procedure avoids the disadvantage by expecting which rule should be used for satisfaction of integrity constraints and starting bottom-up computation based on the expectation. This expectation is not only a technique to scope rule selection but also an indispensable part of our stable model construction because the expectation is done for dynamically generated constraints as well as the constraint for the observation.

A Correct Goal-directed Proof Procedure for a General Logic Program with Integrity Constraints

We present a correct goal-directed procedure for consistent logic program with integrity constraints in stable model semantics [5]. Although there are correct bottom-up procedures for every general logic program [13, 4, 15, 7] to compute stable models, there are no proposed correct goal-directed procedure for every general logic program. Our proposed procedure is correct not only for successful derivation but also for finite failure. This procedure is an extension of Eshghis procedure [3] which is correct for every call-consistent logic program, and can be regarded as a combination of the model elimination procedure [10] and consistency checking in updates of implicit deletions [14].