Dual-normal Logic Programs - the Forgotten Class

TL;DR

This paper explores dual-normal logic programs, a less-studied class of disjunctive answer set programs, analyzing their properties, translations, and complexity, with implications for improving answer set programming solvers.

Contribution

It introduces dual-normal programs, relates them to other classes, and studies their expressive power and complexity, filling a gap in the literature.

Findings

Dual-normal programs can be translated to normal programs.

Dual-normal programs are related to body-cycle free programs.

Complexity results for strong and uniform equivalence are established.

Abstract

Disjunctive Answer Set Programming is a powerful declarative programming paradigm with complexity beyond NP. Identifying classes of programs for which the consistency problem is in NP is of interest from the theoretical standpoint and can potentially lead to improvements in the design of answer set programming solvers. One of such classes consists of dual-normal programs, where the number of positive body atoms in proper rules is at most one. Unlike other classes of programs, dual-normal programs have received little attention so far. In this paper we study this class. We relate dual-normal programs to propositional theories and to normal programs by presenting several inter-translations. With the translation from dual-normal to normal programs at hand, we introduce the novel class of body-cycle free programs, which are in many respects dual to head-cycle free programs. We establish the expressive power of dual-normal programs in terms of SE- and UE-models, and compare them to normal programs. We also discuss the complexity of deciding whether dual-normal programs are strongly and uniformly equivalent.