Abstract
The study of different notions of equivalence is one of the cornerstones of current research in answer-set programming. This is mainly motivated by the needs of program simplification and modular programming, for which ordinary equivalence is insufficient. A recently introduced equivalence notion in this context is hyperequivalence, which includes as special cases strong, uniform, and ordinary equivalence. We study in this paper the question of replacing programs by syntactically simpler ones preserving hyperequivalence (we refer to such a replacement as a casting). In particular, we provide necessary and sufficient semantic conditions under which the elimination of disjunction, negation, or both, in programs is possible, preserving hyperequivalence. In other words, we characterise in model-theoretic terms when a disjunctive logic program can be replaced by a hyperequivalent normal, positive, or Horn program, respectively. Furthermore, we study the computational complexity of the considered tasks and, based on similar results for strong equivalence developed in previous work, we provide methods for constructing the respective hyperequivalent programs. Our results contribute to the understanding of problem settings in logic programming in the sense that they show in which scenarios the usage of certain constructs are superfluous or not.
This work was partially supported by the Austrian Science Fund (FWF) under projects P18019 and P20704.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)
Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385 (1991)
Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Transactions on Computational Logic 2(4), 526–541 (2001)
Eiter, T., Fink, M.: Uniform equivalence of logic programs under the stable model semantics. In: Palamidessi, C. (ed.) ICLP 2003. LNCS, vol. 2916, pp. 224–238. Springer, Heidelberg (2003)
Woltran, S.: A common view on strong, uniform, and other notions of equivalence in answer-set programming. Theory and Practice of Logic Programming 8(2), 217–234 (2008)
Truszczyński, M., Woltran, S.: Relativized hyperequivalence of logic programs for modular programming. In: de la Banda, M.G., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 576–590. Springer, Heidelberg (2008)
Eiter, T., Fink, M., Tompits, H., Woltran, S.: Simplifying logic programs under uniform and strong equivalence. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS, vol. 4483, pp. 87–99. Springer, Heidelberg (2007)
Eiter, T., Fink, M., Tompits, H., Woltran, S.: On eliminating disjunctions in stable logic programming. In: Proc. KR 2004, pp. 447–458. AAAI Press, Menlo Park (2004)
Turner, H.: Strong equivalence made easy: Nested expressions and weight constraints. Theory and Practice of Logic Programming 3(4-5), 602–622 (2003)
Heyting, A.: Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte, physik.-math. Klasse, preußische Akademie der Wissenschaften (1930)
Gödel, K.: Zum intuitionistischen Aussagenkalkül. Anzeiger Akademie der Wissenschaften in Wien, math.-naturwiss. Klasse 69, 65–66 (1932)
Eiter, T., Tompits, H., Woltran, S.: On solution correspondences in answer set programming. In: Proc. IJCAI 2005, pp. 97–102 (2005)
Woltran, S.: Characterizations for relativized notions of equivalence in answer set programming. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS, vol. 3229, pp. 161–173. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pührer, J., Tompits, H., Woltran, S. (2008). Elimination of Disjunction and Negation in Answer-Set Programs under Hyperequivalence. In: Garcia de la Banda, M., Pontelli, E. (eds) Logic Programming. ICLP 2008. Lecture Notes in Computer Science, vol 5366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89982-2_47
Download citation
DOI: https://doi.org/10.1007/978-3-540-89982-2_47
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89981-5
Online ISBN: 978-3-540-89982-2
eBook Packages: Computer ScienceComputer Science (R0)