Complexity Results for Abductive Logic Programming

Thomas Eiter, Georg Gottlob, Nicola Leone

Abstract: In this paper, we argue that logic programming semantics can be more meaningful for abductive reasoning than classical inference by providing examples from the area of knowledge representation and reasoning. The main part of the paper addresses the issue of the computational complexity of the principal decisional problems in abductive reasoning, which are: Given an instance of an abduction problem (i) does the problem have solution (i.e., an explanation); (ii) does a given hypothesis belong to some explanation; and (iii) does a given hypothesis belong to all explanations. These problems are investigated here for the stable model semantics of normal logic programs.