Disjunctive logic programming with negation as failure in the head

Abstract

Disjunctive logic programs have been studied in order to increase expressivity, especially in representing indefinite information. Even though there is no general consensus on any specific semantic for disjunctive logic programs with negation, most of well known semantics are minimal model based. Sometimes real applications need to capture non minimal models, in spite of the fact that they contain redundant information. In representing disjunctive knowledge, for instance, minimal approaches capture exclusive disjunction but they cannot managed the inclusive meaning. The purpose of this paper is to analyze the expressive power of a special combination of disjunctive logic programming, negation as failure (NAF), and strong negation. This class of programs are syntactically uniform, since both kinds of negation are allowed to appear in the head and in the body of a rule, and its semantics allows non minimal models. We introduce a non injective syntactic transformation of disjunctive logic programs with NAF in head into disjunctive logic programs without NAF in head, in order to compare semantically both class of programs. Finally, we prove that the set of answer sets of the transformed disjunctive logic program is strictly included in the set of minimal answer sets of the original program and we discuss its consequences.