A measure of arbitrariness in abductive explanations

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.