Skip to main content
SpringerLink
Log in

Program Correspondence under the Answer-Set Semantics: The Non-ground Case

  • Conference paper
Logic Programming (ICLP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5366))

Included in the following conference series:

Abstract

The study of various notions of equivalence between logic programs in the area of answer-set programming (ASP) gained increasing interest in recent years. The main reason for this undertaking is that ordinary equivalence between answer-set programs fails to yield a replacement property similar to the one of classical logic. Although many refined program correspondence notions have been introduced in the ASP literature so far, most of these notions were studied for propositional programs only, which limits their practical usability as concrete programming applications require the use of variables. In this paper, we address this issue and introduce a general framework for specifying parameterised notions of program equivalence for non-ground disjunctive logic programs under the answer-set semantics. Our framework is a generalisation of a similar one defined previously for the propositional case and allows the specification of several equivalence notions extending well-known ones studied for propositional programs. We provide semantic characterisations for instances of our framework generalising uniform equivalence, and we study decidability and complexity aspects. Furthermore, we consider axiomatisations of such correspondence problems by means of polynomial translations into second-order logic.

This work was partially supported by the Austrian Science Fund (FWF) under grant P18019.

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

Access this chapter

Log in via an institution
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.

References

  1. Leone, N., Pfeifer, G., Faber, W., Eiter, T., Gottlob, G., Perri, S., Scarcello, F.: The DLV System for Knowledge Representation and Reasoning. ACM TOCL 7(3), 499–562 (2006)

    Article  MathSciNet  Google Scholar 

  2. Janhunen, T., Niemelä, I., Seipel, D., Simons, P.: Unfolding Partiality and Disjunctions in Stable Model Semantics. ACM TOCL 7(1), 1–37 (2006)

    Article  MathSciNet  Google Scholar 

  3. Lifschitz, V., Pearce, D., Valverde, A.: Strongly Equivalent Logic Programs. ACM TOCL 2(4), 526–541 (2001)

    Article  MathSciNet  Google Scholar 

  4. 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 

  5. Maher, M.J.: Equivalences of logic programs. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 627–658. Morgan Kaufmann, San Francisco (1988)

    Chapter  Google Scholar 

  6. Sagiv, Y.: Optimizing Datalog Programs. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 659–698. Morgan Kaufmann, San Francisco (1988)

    Chapter  Google Scholar 

  7. 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)

    Chapter  Google Scholar 

  8. Eiter, T., Tompits, H., Woltran, S.: On Solution Correspondences in Answer-Set Programming. In: 19th International Joint Conference on Artificial Intelligence, pp. 97–102 (2005)

    Google Scholar 

  9. Oikarinen, E., Janhunen, T.: Modular Equivalence for Normal Logic Programs. In: 17th European Conference on Artificial Intelligence, pp. 412–416. IOS Press, Amsterdam (2006)

    Google Scholar 

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

    Chapter  Google Scholar 

  11. Lin, F.: Reducing Strong Equivalence of Logic Programs to Entailment in Classical Propositional Logic. In: 8th International Conference on Principles of Knowledge Representation and Reasoning, pp. 170–176. Morgan Kaufmann, San Francisco (2002)

    Google Scholar 

  12. Eiter, T., Fink, M., Tompits, H., Woltran, S.: Strong and Uniform Equivalence in Answer-Set Programming: Characterizations and Complexity Results for the Non-Ground Case. In: 20th National Conference on Artificial Intelligence, pp. 695–700. AAAI Press, Menlo Park (2005)

    Google Scholar 

  13. Lifschitz, V., Pearce, D., Valverde, A.: A Characterization of Strong Equivalence for Logic Programs with Variables. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS, vol. 4483, pp. 188–200. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Oetsch, J., Tompits, H., Woltran, S.: Facts do not Cease to Exist Because They are Ignored: Relativised Uniform Equivalence with Answer-Set Projection. In: 22nd National Conference on Artificial Intelligence, pp. 458–464. AAAI Press, Menlo Park (2007)

    Google Scholar 

  15. Ferraris, P., Lee, J., Lifschitz, V.: A New Perspective on Stable Models. In: 20th International Joint Conference on Artificial Intelligence, pp. 372–379 (2007)

    Google Scholar 

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

    Article  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  18. Shmueli, O.: Decidability and Expressiveness Aspects of Logic Queries. In: 6th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pp. 237–249. ACM, New York (1987)

    Chapter  Google Scholar 

  19. Dantsin, E., Eiter, T., Gottlob, G., Voronkov, A.: Complexity and Expressive Power of Logic Programming. ACM Computing Surveys 33(3), 374–425 (2001)

    Article  Google Scholar 

  20. Eiter, T., Fink, M., Tompits, H., Woltran, S.: Complexity Results for Checking Equivalence of Stratified Logic Programs. In: 20th International Joint Conference on Artificial Intelligence, pp. 330–335 (2007)

    Google Scholar 

  21. McCarthy, J.: Circumscription—A Form of Non-Monotonic Reasoning. Artificial Intelligence 13, 27–39 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  22. Tompits, H., Woltran, S.: Towards Implementations for Advanced Equivalence Checking in Answer-Set Programming. In: Gabbrielli, M., Gupta, G. (eds.) ICLP 2005. LNCS, vol. 3668, pp. 189–203. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Johannes Oetsch & Hans Tompits

Authors
  1. Johannes Oetsch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hans Tompits
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Clayton School of Information Technology, Monash University, Australia

    Maria Garcia de la Banda

  2. Department of Computer Science, New Mexico State University, NM 88003, Las Cruces, USA

    Enrico Pontelli

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Oetsch, J., Tompits, H. (2008). Program Correspondence under the Answer-Set Semantics: The Non-ground Case. 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_49

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-89982-2_49

  • 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)

Publish with us

Policies and ethics

Search

Navigation