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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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References

Balduccini, M., Gelfond, M. and Nogueira, M. 2006. Answer set based design of knowledge systems. Ann. Math. Artif. Intell. 47, 1–2, 183–219.CrossRefGoogle Scholar
Ben-Eliyahu, R. and Dechter, R. 1994. Propositional semantics for disjunctive logic programs. Ann. Math. Artif. Intell. 12, 1–2, 53–87.CrossRefGoogle Scholar
Brewka, G., Eiter, T. and Truszczyński, M. 2011. Answer set programming at a glance. Communications of the ACM 54, 12, 92–103.Google Scholar
Dowling, W. F. and Gallier, J. H. 1984. Linear-time algorithms for testing the satisfiability of propositional Horn formulae. J. Logic Programming 1, 3, 267–284.CrossRefGoogle Scholar
Eiter, T. and Fink, M. 2003. Uniform equivalence of logic programs under the stable model semantics. In Proceedings 19th International Conference on Logic Programming (ICLP 2003). LNCS, vol. 2916. Springer, 224–238.Google Scholar
Eiter, T., Fink, M., Pührer, J., Tompits, H. and Woltran, S. 2013. Model-based recasting in answer-set programming. J. Applied Non-Classical Logics 23, 1–2, 75–104.Google Scholar
Eiter, T., Fink, M., Tompits, H. and Woltran, S. 2004. On eliminating disjunctions in stable logic programming. In Proceedings of the 9th International Conference on Principles of Knowledge Representation and Reasoning (KR 2004). The AAAI Press, 447–458.Google Scholar
Eiter, T., Fink, M. and Woltran, S. 2007. Semantical Characterizations and Complexity of Equivalences in Answer Set Programming. ACM Trans. on Computational Logic 8, 3.Google Scholar
Eiter, T. and Gottlob, G. 1995. On the computational cost of disjunctive logic programming: Propositional case. Ann. Math. Artif. Intell. 15, 3/4, 289–323.CrossRefGoogle Scholar
Fichte, J. K. and Szeider, S. 2013. Backdoors to normality for disjunctive logic programs. In Proceedings of the 27th AAAI Conference on Artificial Intelligence (AAAI 2013). The AAAI Press, 320–327.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T. 2012. Answer Set Solving in Practice. Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan & Claypool Publishers.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical Negation in Logic Programs and Disjunctive Databases. New Generation Comput. 9, 3/4, 365–385.CrossRefGoogle Scholar
Guziolowski, C., Videla, S., Eduati, F., Thiele, S., Cokelaer, T., Siegel, A. and Saez-Rodriguez, J. 2013. Exhaustively characterizing feasible logic models of a signaling network using answer set programming. Bioinformatics 29, 18, 2320–2326. Erratum see Bioinformatics 30, 13, 1942.Google Scholar
Janhunen, T. 2006. Some (in)translatability results for normal logic programs and propositional theories. J. Applied Non-Classical Logics 16, 1–2, 35–86.Google Scholar
Janhunen, T., Niemelä, I., Seipel, D., Simons, P. and You, J.-H. 2006. Unfolding partiality and disjunctions in stable model semantics. ACM Trans. Comput. Log. 7, 1, 1–37.Google Scholar
Lifschitz, V., Pearce, D. and Valverde, A. 2001. Strongly equivalent logic programs. ACM Trans. on Computational Logic 2, 4, 526–541.CrossRefGoogle Scholar
Lifschitz, V. and Woo, T. Y. 1992. Answer sets in general nonmonotonic reasoning. In Proceedings of the 3rd International Conference on Principles of Knowledge Representation and Reasoning (KR 1992). Morgan Kaufmann, 603–614.Google Scholar
Nogueira, M., Balduccini, M., Gelfond, M., Watson, R. and Barry, M. 2001. An A-Prolog decision support system for the Space Shuttle. In Proceedings of the 3rd International Symposium on Practical Aspects of Declarative Language (PADL 2001). LNCS, vol. 1990. Springer, 169–183.Google Scholar
Pearce, D., Tompits, H. and Woltran, S. 2009. Characterising equilibrium logic and nested logic programs: Reductions and complexity. Theory Pract. Log. Program. 9, 5, 565–616.Google Scholar
Przymusinski, T. 1991. Stable semantics for disjunctive programs. New Generation Comput. 9, 401–424.CrossRefGoogle Scholar
Ricca, F., Grasso, G., Alviano, M., Manna, M., Lio, V., Iiritano, S. and Leone, N. 2012. Team-building with answer set programming in the Gioia-Tauro seaport. Theory Pract. Log. Program. 12, 361–381.CrossRefGoogle Scholar
Soininen, T. and Niemelä, I. 1998. Developing a declarative rule language for applications in product configuration. In Proceedings of the 1st International Workshop on Practical Aspects of Declarative Languages (PADL 1999). LNCS, vol. 1551. Springer, 305–319.Google Scholar
Truszczyński, M. 2011. Trichotomy and dichotomy results on the complexity of reasoning with disjunctive logic programs. Theory Pract. Log. Program. 11, 6, 881–904.Google Scholar
Turner, H. 2001. Strong equivalence for logic programs and default theories (made easy). In Proceedings of the 6th International Conference on Logic Programming and Nonmotonic Reasoning (LPNMR 2001), Eiter, T., Faber, W., and Truszczyński, M., Eds. LNCS, vol. 2173. Springer, Vienna, Austria, 81–92.CrossRefGoogle Scholar
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