[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content
Springer Nature Link
Log in

Capturing Stationary and Regular Extensions with Reiter’s Extensions

  • Conference paper
  • First Online:
Logics in Artificial Intelligence (JELIA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1919))

Included in the following conference series:

Abstract

Janhunen et al. [14] have proposed a translation technique for normal logic programs in order to capture the alternating fix-points of a program with the stable models of the translation. The same technique is also applicable in the disjunctive case so that partial stable models can be captured. In this paper, the aim is to capture Przymusinska and Przymusinski’s stationary extensions with Reiter’s extensions using the same translational idea. The resulting translation function is polynomial, but only weakly modular and not perfectly faithful. Fortunately, another technique leads to a polynomial, faithful and modular (PFM) translation function. As a result, stationary default logic (STDL) is ranked in the expressive power hierarchy (EPH) of non-monotonic logics [13]. Moreover, reasoning with stationary extensions as well as brave reasoning with regular extensions (i.e., maximal stationary extensions) can be implemented using an inference engine for reasoning with Reiter’s extensions.

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

Access this chapter

Log in via an institution

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. P.A. Bonatti and T. Eiter. Querying disjunctive database through nonmonotonic logics. Theoretical Computer Science, 160:321–363, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  2. P. Cholewiński, V.W. Marek, A. Mikitiuk, and M. Truszczyński. Computing with default logic. Artificial Intelligence, 112:105–146, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  3. M. Denecker, W. Marek, and M. Truszczyński. Uniform semantic treatment of default and autoepistemic logic. In Principles of Knowledge Representation and Reasoning: Proceedings of the 7th International Conference, pages 74–84, Breckenridge, Colorado, April 2000. Morgan Kaufmann.

    Google Scholar 

  4. J. Dix. Default theories of Poole-type and a method for constructing cumulative versions of default logic. In B. Neumann, editor, Proceedings of the 10th European Conference on AI, pages 289-293, Vienna, Austria, August 1992. Wiley.

    Google Scholar 

  5. M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In Proceedings of the 5th International Conference on Logic Programming, pages 1070–1080, Seattle, USA, August 1988. The MIT Press.

    Google Scholar 

  6. M. Gelfond and V. Lifschitz. Classical negation in logic programs and disjunctive databases. New Generation Computing, 9:365–385, 1991.

    Article  Google Scholar 

  7. G. Gottlob. Complexity results for nonmonotonic logics. Journal of Logic and Computation, 2(3):397–425, June 1992.

    Article  MATH  MathSciNet  Google Scholar 

  8. G. Gottlob. The complexity of default reasoning under the stationary fixed point semantics. Information and Computation, 121:81–92, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  9. G. Gottlob. Translating default logic into standard autoepistemic logic. Journal of the Association for Computing Machinery, 42(2):711–740, 1995.

    MATH  MathSciNet  Google Scholar 

  10. T. Janhunen. Separating disbeliefs from beliefs in autoepistemic reasoning. In J. Dix, U. Furbach, and A. Nerode, editors, Proceedings of the 4th International Conference on Logic Programming and Non-Monotonic Reasoning, pages 132–151, Dagstuhl, Germany, July 1997. Springer-Verlag. LNAI 1265.

    Google Scholar 

  11. T. Janhunen. Non-monotonic systems: A framework for analyzing semantics and structural properties of non-monotonic reasoning. Doctoral dissertation. Research report A49, Helsinki University of Technology, Digital Systems Laboratory, Espoo, Finland, March 1998. 211 p.

    MATH  Google Scholar 

  12. T. Janhunen. Classifying semi-normal default logic on the basis of its expressive power. In M. Gelfond, N. Leone, and G. Pfeifer, editors, Proceedings of the 5th International Conference on Logic Programming and Non-Monotonic Reasoning, LPNMR’99, pages 19–33, El Paso, Texas, December 1999. Springer-Verlag. LNAI.

    Google Scholar 

  13. T. Janhunen. On the intertranslatability of non-monotonic logics. Annals of Mathematics in Artificial Intelligence, 27(1-4):79–128, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  14. T. Janhunen, I. Niemel, P. Simons, and J.-H. You. Unfolding partiality and disjunctions in stable model semantics. In Principles of Knowledge Representation and Reasoning: Proceedings of the 7th International Conference, pages 411–422, Breckenridge, Colorado, April 2000. Morgan Kaufmann.

    Google Scholar 

  15. V. Lifschitz, L.R. Tang, and H. Turner. Nested expressions in logic programs. Annals of Mathematics in Artificial Intelligence, 25:369–389, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  16. W. Marek and M. Truszczyński. Nonmonotonic Logic: Context-Dependent Reasoning. Springer-Verlag, Berlin, 1993.

    MATH  Google Scholar 

  17. J. McCarthy. Circumscription—a form of non-monotonic reasoning. Artificial Intelligence, 13:27–39, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  18. R.C. Moore. Semantical considerations on nonmonotonic logic. Artificial Intelligence, 25:75–94, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  19. H. Przymusinska and T.C. Przymusinski. Stationary default extensions. In Working Notes of the 4th International Workshop on on Nonmonotonic Reasoning, pages 179–193, Plymouth, Vermont, USA, May 1992.

    Google Scholar 

  20. T. Przymusinski. Extended stable semantics for normal and disjunctive logic programs. In Proceedings of the 7th International Conference on Logic Programming, pages 459–477. MIT Press, 1990.

    Google Scholar 

  21. R. Reiter. On closed world data bases. In H. Gallaire and J. Minker, editors, Logic and Data Bases, pages 55–76. Plenum Press, New York, 1978.

    Google Scholar 

  22. R. Reiter. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  23. A. van Gelder. The alternating fixpoints of logic programs with negation. In ACM Symposium on Principles of Database Systems, pages 1–10, 1989.

    Google Scholar 

  24. A. van Gelder, K.A. Ross, and J.S. Schlipf. Unfounded sets and the well-founded semantics for general logic programs, extended abstract. In Proceedings of the 7th Symposium on Principles of Database Systems, pages 221–230, Austin, Texas, March 1988. ACM Press.

    Google Scholar 

  25. A. van Gelder, K.A. Ross, and J.S. Schlipf. The well-founded semantics for generallogic programs. Journal of the ACM, 38(3):620–650, July 1991.

    Article  MATH  Google Scholar 

  26. J.-H. You and L. Yuan. A three-valued semantics for deductive databases and logic programs. Journal of Computer and System Sciences, 49:334–361, 1994.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory for Theoretical Computer Science, Helsinki University of Technology, P.O.Box 5400, FIN-02015 HUT, Finland

    Tomi Janhunen

Authors
  1. Tomi Janhunen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, E.T.S.I. Informática, University of Málaga, 29071, Málaga, Spain

    Manuel Ojeda-Aciego  & Inma P. de Guzmán  & 

  2. Intelligent Systems Department, Computer Science Institute, University of Leipzig, Augustusplatz 10-11, 04109, Leipzig, Germany

    Gerhard Brewka

  3. Center for Artificial Intelligence, Department of Computer Science, University of Lisbon, 2825-114, Caparica, Portugal

    Luís Moniz Pereira

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Janhunen, T. (2000). Capturing Stationary and Regular Extensions with Reiter’s Extensions. In: Ojeda-Aciego, M., de Guzmán, I.P., Brewka, G., Moniz Pereira, L. (eds) Logics in Artificial Intelligence. JELIA 2000. Lecture Notes in Computer Science(), vol 1919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40006-0_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-40006-0_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41131-4

  • Online ISBN: 978-3-540-40006-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation