A Measure of Arbitrariness in Abductive Explanations

Abstract

We study the framework of abductive logic programming extended with integrity constraints. For this framework, we introduce a new measure of the simplicity of an explanation based on its degree of arbitrariness: the more arbitrary the explanation, the less appealing it is, with explanations having no arbitrariness -they are called constrained -being the preferred ones. In the paper, we study basic properties of constrained explanations. For the case when programs in abductive theories are stratified we establish results providing a detailed picture of the complexity of the problem to decide whether constrained explanations exist.

Computing Abductive Explanations

“…Several concepts of simplicity were considered in the literature, most notably those based on minimality with respect to inclusion and cardinality. This paper continues the work of Caroprese et al [5], who studied the problem of "preferred" explanations in the framework of abductive logic programming. Caroprese et al [5] proposed an orthogonal measure of the simplicity (quality) of an explanation which they called the degree of arbitrariness.…”

“…This paper continues the work of Caroprese et al [5], who studied the problem of "preferred" explanations in the framework of abductive logic programming. Caroprese et al [5] proposed an orthogonal measure of the simplicity (quality) of an explanation which they called the degree of arbitrariness. The less arbitrary the explanation (the lower its degree of arbitrariness), the more appealing it is, with explanations having no arbitrariness, called constrained, being the most preferred.…”

“…Caroprese et al [5], [7] formalized these observations into the concept of the degree of arbitrariness. That degree is 1 for the explanations E u , u ̸ ∈ {tom, mary}, E v , v ̸ = dan and E tom,dan and it is 0 for the explanations E tom , E dan , E mary ; they are constrained.…”

“…Also in this case it is essential that the sentence is not based on arbitrary interpretations of the jurors. This paper presents a technique to compute constrained explanations of an observation, following the theoretical framework developed by Caroprese et al [5] for a subclass of abductive theories. It is based on a rewriting of the theory and the observation into a disjunctive logic program with negation.…”

Existential active integrity constraints

“…Constrained updates fulfill the view-update request, changing the database minimally and avoiding arbitrary commitments. A similar approach has been presented for abductive logic programming extended with integrity constraints in Caroprese et al (2014). This work introduces the concept of constrained explanation for an observation as an explanation having no arbitrariness.…”