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.