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Dual-normal logic programs – the forgotten class

Published online by Cambridge University Press:  03 September 2015

JOHANNES K. FICHTE ,
MIROSŁAW TRUSZCZYŃSKI  and
STEFAN WOLTRAN
JOHANNES K. FICHTE
Affiliation:
TU Wien, Austria University of Potsdam, Germany (e-mail: fichte@kr.tuwien.ac.at)
MIROSŁAW TRUSZCZYŃSKI
Affiliation:
University of Kentucky, Lexington, KY, USA (e-mail: mirek@cs.engr.uky.edu)
STEFAN WOLTRAN
Affiliation:
TU Wien, Austria (e-mail: woltran@dbai.tuwien.ac.at)
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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.

Keywords

answer set programmingclasses of logic programsstrong and uniform equivalencepropositional satisfiability
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 15 , Special Issue 4-5: 31st International Conference on Logic Programming , July 2015 , pp. 495 - 510
Copyright
Copyright © Cambridge University Press 2015 

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