Skip to main content
SpringerLink
Log in

Fixpoint Characterizations for Many-Valued Disjunctive Logic Programs with Probabilistic Semantics

  • Conference paper
  • First Online:
Logic Programming and Nonmotonic Reasoning (LPNMR 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2173))

Abstract

In this paper, we continue to explore many-valued disjunctive logic programs with probabilistic semantics. In particular, we newly introduce the least model state semantics for such programs. We show that many-valued disjunctive logic programs under the semantics of minimal models, perfect models, stable models, and least model states can be unfolded to equivalent classical disjunctive logic programs under the respective semantics. Thus, existing technology for classical disjunctive logic programming can be used to implement many-valued disjunctive logic programming. Using these results on unfolding many-valuedness, we then give many-valued fixpoint characterizations for the set of all minimal models and the least model state. We also describe an iterative fixpoint characterization for the perfect model semantics under finite local stratification.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. A. Dekhtyar and V. S. Subrahmanian. Hybrid probabilistic programs. In Proceedings ICLP-97, pp. 391–405. MIT Press, 1997.

    Google Scholar 

  2. J. A. Fernández, J. Lobo, J. Minker, and V. S. Subrahmanian. Disjunctive LP + integrity constraints = stable model semantics. Ann. Math. Artif. Intell., 8(3-4):449–474, 1993. 349

    Article  MATH  Google Scholar 

  3. J. A. Fernández and J. Minker. Bottom-up computation of perfect models for disjunctive theories. J. Logic Program., 25(1):33–51, 1995. 346

    Article  MATH  Google Scholar 

  4. J. Lobo, J. Minker, and A. Rajasekar. Foundations of Disjunctive Logic Programming. MIT Press, Cambridge, MA, 1992. 342, 347

    Google Scholar 

  5. T. Lukasiewicz. Many-valued disjunctive logic programs with probabilistic semantics. In Proceedings LPNMR-99, LNCS 1730, pp. 277–289. Springer, 1999. 336, 337, 339, 340, 341

    Google Scholar 

  6. T. Lukasiewicz. Many-valued first-order logics with probabilistic semantics. In Proceedings CSL-98, LNCS 1584, pp. 415–429. Springer, 1999. 337, 343

    Google Scholar 

  7. T. Lukasiewicz. Probabilistic and truth-functional many-valued logic programming. In Proceedings ISMVL-99, pp. 236–241. IEEE Computer Society, 1999. 337, 343

    Google Scholar 

  8. T. Lukasiewicz. Fixpoint characterizations for many-valued disjunctive logic programs with probabilistic semantics. Technical Report INFSYS RR-1843-01-06, Institut für Informationssysteme, TU Wien, 2001. 337

    Google Scholar 

  9. T. Lukasiewicz. Probabilistic logic programming with conditional constraints. ACM Trans. Computat. Logic, 2(3):289–337, 2001.

    Article  MathSciNet  Google Scholar 

  10. C. Mateis. A Quantitative Extension of Disjunctive Logic Programming. Doctoral Dissertation, Technische Universitäst Wien, 1998.

    Google Scholar 

  11. J. Minker. Overview of disjunctive logic programming. Ann. Math. Artif. Intell., 12:1–24, 1994.

    Article  MathSciNet  Google Scholar 

  12. J. Minker and A. Rajasekar. A fixpoint semantics for disjunctive logic programs. J. Logic Program., 9(1):45–74, 1990. 342, 347

    Article  MathSciNet  MATH  Google Scholar 

  13. R. T. Ng and V. S. Subrahmanian. Stable semantics for probabilistic deductive databases. Inf. Comput., 110:42–83, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  14. L. Ngo. Probabilistic disjunctive logic programming. In Proceedings UAI-96, pp. 397–404. Morgan Kaufmann, 1996.

    Google Scholar 

  15. T. C. Przymusinski. On the declarative semantics of stratified deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pp. 193–216. Morgan Kaufmann, 1988.

    Google Scholar 

  16. T. C. Przymusinski. Stable semantics for disjunctive programs. New Generation Comput., 9:401–424, 1991.

    Article  Google Scholar 

  17. C. Ruiz and J. Minker. Computing stable and partial stable models of extended disjunctive logic programs. In Nonmonotonic Extensions of Logic Programming, LNCS 927, pp. 205–229. Springer, 1995. 349

    Chapter  Google Scholar 

  18. D. Seipel, J. Minker, and C. Ruiz. Model generation and state generation for disjunctive logic programs. J. Logic Program., 32(1):49–69, 1997. 346, 347, 348

    Article  MATH  MathSciNet  Google Scholar 

  19. M. H. van Emden. Quantitative deduction and its fixpoint theory. J. Logic Program., 3(1):37–53, 1986. 337

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut und Ludwig Wittgenstein Labor für Informationssysteme, TU Wien Favoritenstraße 9-11, A-1040, Vienna, Austria

    Thomas Lukasiewics

Authors
  1. Thomas Lukasiewics
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Informationssysteme, Vienna University of Technology, 1040, Wien, Austria

    Thomas Eiter

  2. Institut für Informationssysteme, Vienna University of Technology, 1040, Wien, Austria

    Wolfgang Faber

  3. Department of Computer Science Lexington, University of Kentucky, KY, 40506-0046, USA

    Miros law Truszczyński

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lukasiewics, T. (2001). Fixpoint Characterizations for Many-Valued Disjunctive Logic Programs with Probabilistic Semantics. In: Eiter, T., Faber, W., Truszczyński, M.l. (eds) Logic Programming and Nonmotonic Reasoning. LPNMR 2001. Lecture Notes in Computer Science(), vol 2173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45402-0_25

Download citation

  • DOI: https://doi.org/10.1007/3-540-45402-0_25

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42593-9

  • Online ISBN: 978-3-540-45402-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation