On Equivalence and Inconsistency of Answer Set Programs with External Sources

HEX-programs extend of answer-set programs (ASP) with external sources. In previous work, notions of equivalence of ASP programs under extensions have been developed. Most well-known are strong equivalence, which is given for programs P and Q if P ∪ R and Q ∪ R have the same answer sets for arbitrary programs R, and uniform equivalence, which is given if this is guaranteed for sets R of facts. More finegrained approaches exist, which restrict the set of atoms in the added program R. In this paper we provide a characterization of equivalence of HEX-programs. Since well-known ASP extensions (e.g. constraint ASP) amount to special cases of HEX, the results are interesting beyond the particular formalism. Based on this, we further characterize inconsistency of programs wrt. program extensions. We then discuss possible applications of the results for algorithms improvements.