Replacements in Non-Ground Answer-Set Programming

In this paper, we propose a formal framework for specifying rule replacements in nonmonotonic logic programs within the answer-set programming paradigm. Of particular interest are replacement schemas retaining specific notions of equivalence, among them the prominent notions of strong and uniform equivalence, which have been introduced as theoretical tools for program optimization and verification. We derive some general properties of the replacement framework with respect to these notions of equivalence. Moreover, we generalize results about particular replacement schemas which have been established for ground programs to the non-ground case. Finally, we report a number of complexity results which address the problem of deciding how hard it is to apply a replacement to a given program. Our results provide an important step towards the development of effective optimization methods for non-ground answer-set programming, an issue which has not been addressed much so far.