This paper introduces an abductive framework for updating knowledge bases represented by extended disjunctive programs. We first provide a simple transformation from abductive programs to update programs which are logic programs specifying changes on abductive hypotheses. Then, extended abduction, which was introduced by the same authors as a generalization of traditional abduction, is computed by the answer sets of update programs. Next, different types of updates, view updates and theory updates are characterized by abductive programs and computed by update programs. The task of consistency restoration is also realized as special cases of these updates. Each update problem is comparatively assessed from the computational complexity viewpoint. The result of this paper provides a uniform framework for different types of knowledge base updates, and each update is computed using existing procedures of logic programming.
@cite_2: To explain observations from nonmonotonic background theories, one often needs removal of some hypotheses as well as addition of other hypotheses. Moreover, some observations should not be explained, while some are to be explained. In order to formalize these situations, extended abduction was introduced by Inoue and Sakama (1995) to generalize traditional abduction in the sense that it can compute negative explanations by removing hypotheses and antidexplanations to unexplain negative observations. In this paper, we propose a computational mechanism for extended abduction. When a background theory is written in a normal logic program, we introduce its transaction program for computing extended abduction. A transaction program is a set of nonddeterministic production rules that declaratively specify addition and deletion of abductive hypotheses. Abductive explanations are then computed by the fixpoint of a transaction program using a bottomdup model generation procedure. The correctness of the proposed procedure is shown for the class of acyclic covered abductive logic programs. In the context of deductive databases, a transaction program provides a declarative specification of database update.
Update programs are simple and applied to a broader class of abductive programs, and extended abduction is realized by any procedure for computing answer sets of EDPs. In implementation, some restrictions on programs such as function-free and range-restricted conditions would be necessary. Moreover, since extended abduction includes normal abduction as a special case, update programs are also used for computing normal abduction in EDPs. To compute extended abduction, @cite_2 introduced a transaction program which is a set of production rules to compute (anti-)explanations by fixpoint construction. The procedure works correctly in acyclic covered NLPs. Inoue introduces a simple program transformation from extended abduction to normal abduction in general EDPs. Using the transformation, extended abduction is executed via normal abduction.