Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Characterizations for Relativized Notions of Equivalence in Answer Set Programming

  • Conference paper
Logics in Artificial Intelligence (JELIA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3229))

Included in the following conference series:

Abstract

Recent research in nonmonotonic logic programming focuses on alternative notions of equivalence. In particular, strong and uniform equivalence are both proposed as useful tools to optimize (parts of) a logic program. More specifically, given a set P of program rules and a possible optimization Q, strong (resp. uniform) equivalence requires that adding any set S of rules (resp. facts) to P and Q simultaneously results in equivalent programs, i.e., P∪ S and Q∪ S possess the same stable models. However, in practice it is often necessary to relax this condition in such a way, that dedicated internal atoms in P or Q are no longer allowed to occur in the possible extensions S. In this paper, we consider these relativized notions of both uniform and strong equivalence and provide semantical characterizations by generalizing the notions of UE- and SE-modelhood. These new characterizations capture all notions of equivalence including ordinary equivalence in a uniform way. Finally, we analyze the complexity of the introduced equivalence tests for the important classes of normal and disjunctive logic programs. As a by-product, we reduce the tests for relativized equivalences to ordinary equivalence between two programs. These reductions may serve as a basis for implementation.

Supported by the Austrian Science Fund (FWF) under project P15068-INF and by the European Commission under projects FET-2001-37004 WASP and IST-2001-33570 INFOMIX.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Bidoit, N., Froidevaux, C.: General Logical Databases and Programs: Default Logic Semantics and Stratification. Information and Computation 91, 15–54 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  2. Brass, S., Dix, J.: Semantics of (Disjunctive) Logic Programs Based on Partial Evaluation. Journal of Logic Programming 38(3), 167–213 (1999)

    Google Scholar 

  3. Cabalar, P.: A Three-Valued Characterization for Strong Equivalence of Logic Programs. In: Proc. AAAI 2002, pp. 106–111. AAAI Press/MIT Press (2002)

    Google Scholar 

  4. de Jongh, D., Hendriks, L.: Characterizations of Strongly Equivalent Logic Programs in Intermediate Logics. Theory and Practice of Logic Programming 3(3), 259–270 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Eiter, T., Faber, W., Leone, N., Pfeifer, G.: Declarative Problem-Solving Using the DLV System. In: Logic-Based Artificial Intelligence, pp. 79–103. Kluwer Academic, Dordrecht (2000)

    Google Scholar 

  6. 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)

    Chapter  Google Scholar 

  7. Eiter, T., Fink, M., Tompits, H., Woltran, S.: On Eliminating Disjunctions in Stable Logic Programming. In: Proc. KR 2004, pp. 447–585. AAAI-Press, Menlo Park (2004)

    Google Scholar 

  8. Eiter, T., Fink, M., Tompits, H., Woltran, S.: Simplifying Logic Programs under Uniform and Strong Equivalence. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 87–99. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  9. Eiter, T., Gottlob, G.: On the Computational Cost of Disjunctive Logic Programming: Propositional Case. Annals of Math. and Artificial Intelligence 15(3/4), 289–323 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Eiter, T., Gottlob, G., Mannila, H.: Disjunctive Datalog. ACM Transactions on Database Systems 22, 364–418 (1997)

    Article  Google Scholar 

  11. Gelfond, M., Lifschitz, V.: ClassicalNegation in Logic Programs and Disjunctive Databases. New Generation Computing 9, 365–385 (1991)

    Article  Google Scholar 

  12. Inoue, K., Sakama, C.: Equivalence of Logic Programs under Updates. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 174–186. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Janhunen, T., Niemelä, I., Simons, P., You, J.-H.: Partiality and Disjunctions in Stable Model Semantics. In: Proc. KR 2000, pp. 411–419. Morgan Kaufmann, San Francisco (2000)

    Google Scholar 

  14. Janhunen, T., Oikarinen, E.: LPEQ and DLPEQ - Translators for Automated Equivalence Testing of Logic Programs. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 336–340. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  15. Lifschitz, V., Pearce, D., Valverde, A.: Strongly Equivalent Logic Programs. ACM Transactions on Computational Logic 2(4), 526–541 (2001)

    Article  MathSciNet  Google Scholar 

  16. Lifschitz, V., Turner, H.: Splitting a Logic Program. In: Proc. ICLP 1994, pp. 23–38 (1994)

    Google Scholar 

  17. Lin, F.: Reducing Strong Equivalence of Logic Programs to Entailment in Classical Propositional Logic. In: Proc. KR 2002, pp. 170–176. Morgan Kaufmann, San Francisco (2002)

    Google Scholar 

  18. Maher, M.J.: Equivalences of Logic Programs. In: Minker [20], pp. 627–658

    Google Scholar 

  19. Marek, W., Truszczyński, M.: Autoepistemic Logic. J. of the ACM 38(3), 588–619 (1991)

    Article  MATH  Google Scholar 

  20. Minker, J. (ed.): Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann, San Francisco (1988)

    Google Scholar 

  21. Oikarinen, E., Janhunen, T.: Verifying the Equivalence of Logic programs in the Disjunctive Case. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 180–193. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  22. 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)

    Chapter  Google Scholar 

  23. Pearce, D., Tompits, H., Woltran, S.: Encodings for Equilibrium Logic and Logic Programs with Nested Expressions. In: Brazdil, P.B., Jorge, A.M. (eds.) EPIA 2001. LNCS (LNAI), vol. 2258, pp. 306–320. Springer, Heidelberg (2001)

    Google Scholar 

  24. Pearce, D., Valverde, A.: Uniform Equivalence for Equilibrium Logic and Logic Programs. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 194–206. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  25. Przymusinski, T.: Stable Semantics for Disjunctive Programs. New Generation Computing Journal 9, 401–424 (1991)

    Article  Google Scholar 

  26. Sagiv, Y.: Optimizing Datalog Programs. In: Minker [20], pp. 659–698

    Google Scholar 

  27. Shmueli, O.: Equivalence of Datalog Queries is Undecidable. Journal of Logic Programming 15(3), 231–242 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  28. Turner, H.: Strong Equivalence for Logic Programs and Default Theories (Made Easy). In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 81–92. Springer, Heidelberg (2001)

    Google Scholar 

  29. Turner, H.: Strong Equivalence Made Easy: Nested Expressions and Weight Constraints. Theory and Practice of Logic Programming 3(4-5), 602–622 (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informationssysteme 184/3, Technische Universität Wien, Favoritenstraße 9-11, A-1040, Vienna, Austria

    Stefan Woltran

Authors
  1. Stefan Woltran
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. CENTRIA, Universidade Nova de Lisboa, Portugal

    Jóse Júlio Alferes

  2. Departamento de Informática, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    João Leite

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Woltran, S. (2004). Characterizations for Relativized Notions of Equivalence in Answer Set Programming. In: Alferes, J.J., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2004. Lecture Notes in Computer Science(), vol 3229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30227-8_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30227-8_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23242-1

  • Online ISBN: 978-3-540-30227-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation