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 \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).) 
Luciano Caroprese, Irina Trubitsyna, Miroslaw Truszczynski and Ester   Zumpano
cs.LO