P-stable models of strong kernel programs

The research community has long recognized the study of non-monotonic reasoning (NMR) as a promising approach to model features of commonsense reasoning. We study one of the semantics that are useful to formalize NMR, called the p-stable semantics. We introduce three different formats for normal programs: negative normal programs, restricted negative normal programs and strong kernel programs. These forms help to simplify the search of p-stable models of the original program. One of the main results of this paper indicates that the p-stable semantics for strong kernel programs is the same as the stable semantics. This way, all the applications based on stable semantics for those kernel programs (defined in [S. Costantini, A. Provetti, Normal forms for answer set programming, J. Theory Pract. Log. Program. 5 (2005) 747–760]) that are strong kernel programs can also be based on the p-stable semantics.