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Relativized hyperequivalence of logic programs for modular programming

Published online by Cambridge University Press:  14 September 2009

MIROSŁAW TRUSZCZYŃSKI  and
STEFAN WOLTRAN
MIROSŁAW TRUSZCZYŃSKI
Affiliation:
Department of Computer Science, University of Kentucky, Lexington, KY 40506-0046, USA (e-mail: [email protected])
STEFAN WOLTRAN
Affiliation:
Institute of Information Systems 184/2, Technische Universität Wien, Favoritenstrasse 9-11, 1040 Vienna, Austria (e-mail: [email protected])
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Abstract

A recent framework of relativized hyperequivalence of programs offers a unifying generalization of strong and uniform equivalence. It seems to be especially well suited for applications in program optimization and modular programming due to its flexibility that allows us to restrict, independently of each other, the head and body alphabets in context programs. We study relativized hyperequivalence for the three semantics of logic programs given by stable, supported, and supported minimal models. For each semantics, we identify four types of contexts, depending on whether the head and body alphabets are given directly or as the complement of a given set. Hyperequivalence relative to contexts where the head and body alphabets are specified directly has been studied before. In this paper, we establish the complexity of deciding relativized hyperequivalence with respect to the three other types of context programs.

Keywords

answer-set programmingstrong equivalenceuniform equivalencerelativized equivalencestable modelssupported modelsminimal modelscomplexity
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 9 , Issue 6 , November 2009 , pp. 781 - 819
Copyright
Copyright © Cambridge University Press 2009

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References

Apt, K. 1990. Logic programming. In Handbook of Theoretical Computer Science, Volume B: Formal Models and Semantics, van Leeuven, J., Ed. Elsevier, Amsterdam, 493–574.Google Scholar
Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge, UK.CrossRefGoogle Scholar
Brass, S. and Dix, J. 1997. Characterizations of the disjunctive stable semantics by partial evaluation. Journal of Logic Programming 32, 3, 207–228.CrossRefGoogle Scholar
Cabalar, P., Odintsov, S., Pearce, D. and Valverde, A. 2006. Analysing and extending well-founded and partial stable semantics using partial equilibrium logic. In Proc. of the 22nd International Conference (ICLP 2006), Etalle, S. and Truszczyński, M., Eds. Lecture Notes in Computer Science, Vol. 4079. Springer, Berlin, 346–360.Google Scholar
Clark, K. 1978. Negation as failure. In Logic and Data Bases, Gallaire, H. and Minker, J., Eds. Plenum Press, New York and London, 293–322.CrossRefGoogle Scholar
de Jongh, D. and Hendriks, L. 2003. Characterizations of strongly equivalent logic programs in intermediate logics. Theory and Practice of Logic Programming 3, 3, 259–270.CrossRefGoogle Scholar
Eiter, T. and Fink, M. 2003. Uniform equivalence of logic programs under the stable model semantics. In Proc. of the 19th International Conference on Logic Programming (ICLP 2003), Palamidessi, C., Ed. Lecture Notes in Computer Science, Vol. 2916. Springer, Berlin, 224–238.Google Scholar
Eiter, T., Fink, M. and Woltran, S. 2007. Semantical characterizations and complexity of equivalences in answer set programming. ACM Transactions on Computational Logic 8, 3, Paper 17.CrossRefGoogle Scholar
Eiter, T. and Gottlob, G. 1995. On the computational cost of disjunctive logic programming: Propositional case. Annals of Mathematics and Artificial Intelligence 15, 3–4, 289–323.CrossRefGoogle Scholar
Eiter, T., Tompits, H. and Woltran, S. 2005. On solution correspondences in answer-set programming. In Proc. of the 19th International Joint Conference on Artificial Intelligence (IJCAI 2005), Kaelbling, L. P. and Saffiotti, A., Eds. Professional Book Center, Denver, 97–102.Google Scholar
Erdogan, S. and Lifschitz, V. 2004. Definitions in answer set programming (extended abstract). In Proc. of the 7th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2004), Lifschitz, V. and Niemelä, I., Eds. Lecture Notes in Computer Science, Vol. 2916. Springer, Berlin, 483–484.Google Scholar
Gaifman, H. and Shapiro, E. 1989. Fully abstract compositional semantics for logic programs. In Proc. of the 16th Annual ACM Symposium on Principles of Programming Languages (POPL 1989). ACM, New York, 134–142.Google Scholar
Gebser, M., Liu, L., Namasivayam, G., Neumann, A., Schaub, T. and Truszczyński, M. 2007. The first answer set programming system competition. In Proc. of the 9th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2007), Baral, C., Brewka, G. and Schlipf, J., Eds. Lecture Notes in Computer Science, Vol. 4483. Springer, Berlin, 3–17.CrossRefGoogle Scholar
Gelfond, M. 2002. Representing knowledge in A-Prolog. In Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part II, Kakas, A. and Sadri, F., Eds. Lecture Notes in Computer Science, Vol. 2408. Springer, Berlin, 413–451.CrossRefGoogle Scholar
Gelfond, M. and Leone, N. 2002. Logic programming and knowledge representation – The A-prolog perspective. Artificial Intelligence 138, 1–2, 3–38.CrossRefGoogle Scholar
Inoue, K. and Sakama, C. 1998. Negation as failure in the head. Journal of Logic Programming 35, 39–78.CrossRefGoogle Scholar
Inoue, K. and Sakama, C. 2004. Equivalence of logic programs under updates. In Proc. of the 9th European Conference on Logics in Artificial Intelligence (JELIA 2004), Alferes, J. and Leite, J., Eds. Lecture Notes in Computer Science, Vol. 3229. Springer, Berlin, New York, 174–186.Google Scholar
Janhunen, T. 2006. Some (in)translatability results for normal logic programs and propositional theories. Journal of Applied Non-Classical Logics 16, 1–2, 35–86.CrossRefGoogle Scholar
Janhunen, T., Oikarinen, E., Tompits, H. and Woltran, S. 2007. Modularity aspects of disjunctive stable models. In Proc. of the 9th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR 2007), Baral, C., Brewka, G. and Schlipf, J., Eds. Lecture Notes in Artificial Intelligence, Vol. 4483. Springer, Berlin, 175–187.CrossRefGoogle Scholar
Lifschitz, V., Pearce, D. and Valverde, A. 2001. Strongly equivalent logic programs. ACM Transactions on Computational Logic 2, 4, 526–541.CrossRefGoogle Scholar
Lifschitz, V. and Turner, H. 1994. Splitting a logic program. In Proc. of the 11th International Conference on Logic Programming (ICLP 1994), Hentenryck, P. V., Ed. MIT Press, Cambridge, MA, 23–37.Google Scholar
Lin, F. 2002. Reducing strong equivalence of logic programs to entailment in classical propositional logic. In Proc. of the 8th International Conference on Principles of Knowledge Representation and Reasoning (KR 2002), Fensel, D., McGuinness, D. and Williams, M.-A., Eds. Morgan Kaufmann, San Francisco, 170–176.Google Scholar
Marek, V. and Truszczyński, M. 1999. Stable models and an alternative logic programming paradigm. In The Logic Programming Paradigm: A 25-Year Perspective, Apt, K., Marek, W., Truszczyński, M. and Warren, D., Eds. Springer, Berlin, 375–398.Google Scholar
Niemelä, I. 1999. Logic programming with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 3–4, 241–273.CrossRefGoogle Scholar
Oetsch, J., Tompits, H. and Woltran, S. 2007. Facts do not cease to exist because they are ignored: Relativised uniform equivalence with answer-set projection. In Proc. of the 22nd National Conference on Artificial Intelligence (AAAI 2007). AAAI Press, Menlo Park, CA, 458–464.Google Scholar
Oikarinen, E. and Janhunen, T. 2006. Modular equivalence for normal logic programs. In Proc. of the 17th European Conference on Artificial Intelligence (ECAI 2006), Vol. 141, Brewka, G., Coradeschi, S., Perini, A. and Traverso, P., Eds. IOS Press, Amsterdam, 412–416.Google Scholar
Sagiv, Y. 1988. Optimizing datalog programs. In Foundations of Deductive Databases and Logic Programming, Minker, J., Ed. Morgan Kaufmann, San Francisco, 659–698.CrossRefGoogle Scholar
Truszczyński, M. and Woltran, S. 2008. Hyperequivalence of logic programs with respect to supported models. Annals of Mathematics and Artificial Intelligence 53, 1–4, 331–365.CrossRefGoogle Scholar
Turner, H. 2003. Strong equivalence made easy: Nested expressions and weight constraints. Theory and Practice of Logic Programming 3, 4–5, 609–622.CrossRefGoogle Scholar
Woltran, S. 2004. Characterizations for relativized notions of equivalence in answer set programming. In Proc. of the 9th European Conference on Logics in Artificial Intelligence (JELIA 2004), Alferes, J. and Leite, J., Eds. Lecture Notes in Computer Science, Vol. 3229. Springer, Berlin, 161–173.Google Scholar
Woltran, S. 2008. 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.Google Scholar