Abstract
Recent research in answer-set programming (ASP) is concerned with the problem of finding faithful transformations of logic programs under the stable semantics. This is in particular relevant in practice when programs with variables are considered, where such transformations play a basic role in (offline) simplifications of logic programs. So far, such transformations of non-ground programs have been considered under the implicit assumption that the domain (i.e., the set of constants of the underlying language) is always suitably extensible. However, this may not be a desired scenario, e.g., if one needs to deal with a fixed number of objects. In this paper, we investigate how an explicit restriction of the domain influences the applicability of program transformations and we study in detail computational aspects for the concepts of tautological rules and rule subsumption. More precisely, we provide a full picture of the complexity to decide whether a non-ground rule is tautological or subsumed by another rule under several restrictions.
This work was partially supported by the Austrian Science Fund (FWF) under project P18019.
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References
Eiter, T., et al.: Strong and Uniform Equivalence in Answer-Set Programming: Characterizations and Complexity Results for the Non-Ground Case. In: Proc. AAAI’05, pp. 695–700. AAAI Press, Menlo Park (2005)
Lifschitz, V., Pearce, D., Valverde, A.: Strongly Equivalent Logic Programs. ACM Transactions on Computational Logic 2(4), 526–541 (2001)
Brass, S., Dix, J.: Semantics of (Disjunctive) Logic Programs Based on Partial Evaluation. Journal of Logic Programming 38(3), 167–213 (1999)
Osorio, M., Navarro, J.A., Arrazola, J.: Equivalence in Answer Set Programming. In: Pettorossi, A. (ed.) LOPSTR 2001. LNCS, vol. 2372, pp. 57–75. Springer, Heidelberg (2002)
Inoue, K., Sakama, C.: Equivalence of Logic Programs Under Updates. In: Alferes, J.J., Leite, J.A. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 174–186. Springer, Heidelberg (2004)
Lin, F., Chen, Y.: Discovering Classes of Strongly Equivalent Logic Programs. In: Proc. IJCAI’05, pp. 516–521 (2005)
Eiter, T., et al.: Replacements in Non-Ground Answer-Set Programming. In: Proc. KR’06, pp. 340–351. AAAI Press, Menlo Park (2006)
Lassez, J.L., Marriott, K.: Explicit Representation of Terms Defined by Counter Examples. Journal of Automated Reasoning 3(3), 301–317 (1987)
Kunen, K.: Answer Sets and Negation as Failure. In: Proc. ICLP’87, pp. 219–228. MIT Press, Cambridge (1987)
Kapur, D., et al.: Sufficient-Completeness, Ground-Reducibility and their Complexity. Acta Informatica 28(4), 311–350 (1991)
Gelfond, M., Lifschitz, V.: Classical Negation in Logic Programs and Disjunctive Databases. New Generation Computing 9, 365–385 (1991)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)
Wang, K., Zhou, L.: Comparisons and Computation of Well-founded Semantics for Disjunctive Logic Programs. ACM Transactions on Computational Logic 6(2), 295–327 (2005)
Traxler, P.: Techniques for Simplifying Disjunctive Datalog Programs with Negation. Master’s thesis, Technische Universität Wien, Institut für Informationssysteme (2006)
Pichler, R.: On the Complexity of H-Subsumption. In: Gottlob, G., Grandjean, E., Seyr, K. (eds.) CSL 1998. LNCS, vol. 1584, pp. 355–371. Springer, Heidelberg (1999)
Eiter, T., et al.: Complexity of Answer Set Checking and Bounded Predicate Arities for Non-ground Answer Set Programming. In: Proc. KR’04, pp. 377–387. AAAI Press, Menlo Park (2004)
Vardi, M.: On the Complexity of Bounded-Variable Queries. In: Proc. PODS’95, pp. 266–276 (1995)
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Fink, M., Pichler, R., Tompits, H., Woltran, S. (2007). Complexity of Rule Redundancy in Non-ground Answer-Set Programming over Finite Domains. In: Baral, C., Brewka, G., Schlipf, J. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2007. Lecture Notes in Computer Science(), vol 4483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72200-7_12
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DOI: https://doi.org/10.1007/978-3-540-72200-7_12
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