Explaining Inconsistency in Answer Set Programs and Extensions.

Answer Set Programming (ASP) is a well-known problem solving approach based on nonmonotonic logic programs. hex-programs extend ASP with external atoms for accessing arbitrary external information. In this paper we study inconsistent ASP-and hex-programs, i.e., programs which do not possess answer sets, and introduce a novel notion of inconsistency reasons for characterizing their inconsistency depending on the input facts. This problem is mainly motivated by upcoming applications for optimizations of the evaluation algorithms for hex-programs. Further applications can be found in ASP debugging. We then analyze the complexity of reasoning problems related to the computation of such inconsistency reasons. Finally, we present a meta-programming encoding in disjunctive ASP which computes inconsistency reasons for given normal logic programs, and a basic procedural algorithm for computing inconsistency reasons for general hex-programs.