A Measure of Arbitrariness in Abductive Explanations

TL;DR

This paper introduces a new measure of arbitrariness to evaluate the simplicity of abductive explanations, favoring constrained explanations with less arbitrariness, and analyzes their properties and complexity in stratified programs.

Contribution

It proposes a novel arbitrariness measure for abductive explanations and studies their properties and complexity in stratified logic programs.

Findings

Constrained explanations have desirable properties.

Deciding the existence of constrained explanations is complex in stratified programs.

The measure helps identify more meaningful 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 \emph{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. (To appear in Theory and Practice of Logic Programming (TPLP).)