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_38: Abstract In order to express incomplete knowledge, extended logic programs have been proposed as logic programs with classical negation along with negation as failure. This paper discusses ways to deal with a broad class of common sense knowledge by using extended logic programs. For this purpose, we present a uniform approach for dealing with both incomplete and contradictory programs, as a simple framework of hypothetical reasoning in which some rules are dealt with as candidate hypotheses that can be used to augment the background theory. This theory formation framework can be used for default reasoning, contradiction removals, the closed world assumption, and abduction. We also show a translation of the theory formation framework to an extended logic program whose answer sets correspond to the consistent belief sets of augmented theories.
@cite_27: This paper proposes a method of nonmonotonic theory change. We first introduce a new form of abduction that can account for observations in nonmonotonic situation. Then we provide a framework of autoepistemic update, which describes nonmonotonic theory change through the extended abductive framework. The proposed update semantics is fairly general and provides a unified framework for various update semantics such as first-order update, view update of databases, and contradiction removal of nonmonotonic theories.
Inoue characterizes inconsistency resolution in an ELP @math by the abductive program @math . Then, he considers a maximal consistent subset of the hypotheses @math , which is computed using a program transformation from the abductive program to an ELP. We characterized the same problem by the abductive program @math in , but the result is the same as @cite_38 for ELPs. The problem is also characterized by the abductive program @math in @cite_27 . This formulation, however, produces different results in general. For instance, given the inconsistent program @math , @math has the minimal explanation @math which produces the updated program @math . On the other hand, @math has the minimal explanation @math and the result of update is @math . Thus, @math permits the introduction of new facts as well as the deletion of facts to resolve inconsistency. Generally, permitting introduction of sentences increases the number of possible solutions. Nevertheless, this type of inconsistency resolution is also realized by computing consistent U-minimal answer sets of the update program of @math .