# Dual-normal Logic Programs - the Forgotten Class

arXiv: https://arxiv.org/abs/1507.05388 · HTML: https://mlsanity.com/paper/1507.05388/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2015.

## Built on by (most cited first, 3 of 3)

- [Sequential composition of answer set programs](https://mlsanity.com/paper/2104.12156/) (2021)
- [On the Configuration of More and Less Expressive Logic Programs](https://mlsanity.com/paper/2203.01024/) (2022)
- [Epistemic Logic Programs: Non-Ground and Counting Complexity](https://mlsanity.com/paper/2503.04731/) (2025)

## Abstract (arXiv)

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.