Computing Abductive Explanations

Abstract

We study the computation of constrained explanations in the framework of abductive logic programming. A general characteristic of abductive reasoning is the existence of multiple abductive explanations. Therefore, identifying a subclass of “preferred explanations” is a relevant problem. A typical approach is to “prefer” explanations that are, in some sense, simple. Several concepts of simplicity were considered in the literature, most notably those based on minimality with respect to inclusion and cardinality. We adopt, as a measure of the quality of an explanation, its degree of arbitrariness that can be briefly described as the number of arbitrary assumptions that have been made to derive the explanation. The more arbitrary the explanation, the less appealing it is, with explanations having no arbitrariness, called constrained, being the preferred ones. In this article, we present a technique that, for a special class of theories, computes constrained explanations. It is based on a rewriting of the theory and the observation into a disjunctive logic program with negation so that the constrained explanations correspond to a subset of its stable models. The proposed technique lays the foundation for using ASP solvers to compute constrained explanations.