Signed logic programs

TL;DR: It is shown that even for programs with classical negation and disjunc-tion the existence of a signing is a simple syntactic criterion that can guarantee several types of good behavior: consistency, coincidence of consequences under answer set and well-founded semantics, existence of answer sets expressible in terms of the well- founded model and a signing for the program.

Abstract: In this paper we explore the notion of a \signing" of a logic program, in the framework of the answer set semantics. In particular, we generalize and extend the notion of a signing, and show that even for programs with classical negation and disjunc-tion the existence of a signing is a simple syntactic criterion that can guarantee several diierent sorts of good behavior: consistency, coincidence of consequences under answer set and well-founded semantics, existence of \standard" answer sets expressible in terms of the well-founded model and a signing for the program, and a restricted monotonicity property. The key technical result in this paper is a theorem relating the consequences of a signed disjunctive program with classical negation to the consequences of the members of a closely related family of signed nondisjunc-tive programs. These nondisjunctive programs are the \covers" of the disjunctive program, where a cover is any program that can be obtained by removing all but one literal from the head of each rule in the disjunctive program. To illustrate the usefulness of these results, we apply them to a family of programs for reasoning about action.