On Solution Correspondences in Answer-Set Programming

We introduce a general framework for specifying program correspondence under the answer-set semantics. The framework allows to define different kinds of equivalence notions, including previously defined notions like strong and uniform equivalence, in which programs are extended with rules from a given context, and correspondence is determined by means of a binary relation. In particular, refined equivalence notions based on projected answer sets can be defined within this framework, where not all parts of an answer set are of relevance. We study general characterizations of inclusion and equivalence problems, introducing novel semantical structures. Furthermore, we deal with the issue of determining counterexamples for a given correspondence problem, and we analyze the computational complexity of correspondence checking.