Skip to main content
SpringerLink
Log in

The Well-Founded Semantics in Normal Logic Programs with Uncertainty

  • Conference paper
  • First Online:
Functional and Logic Programming (FLOPS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2441))

Included in the following conference series:

Abstract

Many frameworks of logic programming have been proposed to manage uncertain information in deductive databases and expert systems. Roughly, on the basis of how uncertainty is associated to facts and the rules in a program, they can be classified into implication-based (IB) and annotation-based (AB). However, one fundamental issue that remains unaddressed in the IB approach is the representation and the manipulation of the non-monotonic mode of negation, an important feature for real applications. Our focus in this paper is to introduce non-monotonic negation in the parametric IB framework, a unifying umbrella for IB frameworks. The semantical approach that we will adopt is based on the well-founded semantics, one of the most widely studied and used semantics of (classical) logic programs with negation.

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. Fahiem Bacchus. Representing and Reasoning with Probabilistic Knowledge. The MIT Press, 1990. 152

    Google Scholar 

  2. True H. Cao. Annotated fuzzy logic programs. Fuzzy Sets and Systems, 113(2):277–298, 2000. 152

    Article  MATH  MathSciNet  Google Scholar 

  3. K. L. Clark. On closed world data bases. In Hervé Gallaire and Jack Minker, editors, Logic and data bases, pages 293–322. Plenum Press, New York, NY, 1978. 153

    Google Scholar 

  4. Alex Dekhtyar and V. S. Subrahmanian. Hybrid probabilistic programs. In Proc. of the 13th Int. Conf. on Logic Programming (ICLP-97), Leuven, Belgium, 1997. The MIT Press. 152

    Google Scholar 

  5. Didier Dubois, Jérome Lang, and Henri Prade. Towards possibilistic logic programming. In Proc. of the 8th Int. Conf. on Logic Programming (ICLP-91), pages 581–595. The MIT Press, 1991. 152, 153

    Google Scholar 

  6. Didier Dubois and Henri Prade. Approximate and commonsense reasoning: From theory to practice. In Zbigniew W. Ras and Michalewicz Maciek, editors, Proc. of the 9th Int. Sym. on Methodologies for Intelligent Systems (ISMIS-96), number 1079 in Lecture Notes in Artificial Intelligence, pages 19–33. Springer-Verlag, 1996. 152

    Google Scholar 

  7. Gonzalo Escalada-Imaz and Felip Manyà. Efficient interpretation of propositional multiple-valued logic programs. In Proc. of the 5th Int. Conf. on Information Processing and Managment of Uncertainty in Knowledge-Based Systems, (IPMU-94), number 945 in Lecture Notes in Computer Science, pages 428–439. Springer-Verlag, 1994. 153

    Google Scholar 

  8. M.C. Fitting. The family of stable models. Journal of Logic Programming, 17:197–225, 1993. 159

    Article  MATH  MathSciNet  Google Scholar 

  9. Melvin Fitting. Bilattices and the semantics of logic programming. Journal of Logic Programming, 11:91–116, 1991. 152, 153

    Article  MATH  MathSciNet  Google Scholar 

  10. Norbert Fuhr. Probabilistic datalog: Implementing logical information retrieval for advanced applications. Journal of the American Society for Information Science, 51(2):95–110, 2000. 152

    Article  MathSciNet  Google Scholar 

  11. Allen Van Gelder. The alternating fixpoint of logic programs with negation. In Proc. of the 8th ACM SIGACT SIGMOD Sym. on Principles of Database Systems (PODS-89), pages 1–10, 1989. 154, 160, 161, 163

    Google Scholar 

  12. M. Gelfond and V. Lifschitz. Logic programs with classical negation. In David H.D. Warren and Peter Szeredi, editors, Proceedings of the Seventh International Conference on Logic Programming, pages 579–597, Jerusalem, 1990. The MIT Press. 153

    Google Scholar 

  13. Michael Gelfond, Halina Przymusinska, and Teodor C. Przymusinski. On the relationship between circumscription and negation as failure. Artificial Intelligence, 38:75–94, 1989. 153

    Article  MATH  MathSciNet  Google Scholar 

  14. Mitsuru Ishizuka and Naoki Kanai. Prolog-ELF: incorporating fuzzy logic. In Proc. of the 9th Int. Joint Conf. on Artificial Intelligence (IJCAI-85), pages 701–703, Los Angeles, CA, 1985. 152

    Google Scholar 

  15. M. Kifer and Ai Li. On the semantics of rule-based expert systems with uncertainty. In Proc. of the Int. Conf. on Database Theory (ICDT-88), number 326 in Lecture Notes in Computer Science, pages 102–117. Springer-Verlag, 1988. 152, 153

    Google Scholar 

  16. Michael Kifer and V. S. Subrahmanian. Theory of generalized annotaded logic programming and its applications. Journal of Logic Programming, 12:335–367, 1992. 152, 153

    Article  MathSciNet  Google Scholar 

  17. R. Kruse, E. Schwecke, and J. Heinsohn. Uncertainty and Vagueness in Knowledge Based Systems. Springer-Verlag, Berlin, Germany, 1991. 152

    MATH  Google Scholar 

  18. Laks Lakshmanan. An epistemic foundation for logic programming with uncertainty. In Foundations of Software Technology and Theoretical Computer Science, number 880 in Lecture Notes in Computer Science, pages 89–100. Springer-Verlag, 1994. 152, 153

    Google Scholar 

  19. Laks V. S. Lakshmanan and Nematollaah Shiri. Probabilistic deductive databases. In Int’l Logic Programming Symposium, pages 254–268, 1994. 152, 153

    Google Scholar 

  20. Laks V. S. Lakshmanan and Nematollaah Shiri. A parametric approach to deductive databases with uncertainty. IEEE Transactions on Knowledge and Data Engineering, 13(4):554–570, 2001. 152, 153, 154, 155, 159, 162, 163

    Article  Google Scholar 

  21. James J. Lu. Logic programming with signs and annotations. Journal of Logic and Computation, 6(6):755–778, 1996. 152

    Article  MATH  MathSciNet  Google Scholar 

  22. Thomas Lukasiewicz. Probabilistic logic programming. In Proc. of the 13th European Conf. on Artificial Intelligence (ECAI-98), pages 388–392, Brighton (England), August 1998. 152

    Google Scholar 

  23. John McCarthy. Circumscription — a form of nonmonotonic reasoning. Artificial Intelligence, 13:27–39, 1980. 153

    Article  MATH  MathSciNet  Google Scholar 

  24. Jack Minker. On indefinite data bases and the closed world assumption. In Springer-Verlag, editor, Proc. of the 6th Conf. on Automated Deduction (CADE-82), number 138 in Lecture Notes in Computer Science, 1982. 153

    Chapter  Google Scholar 

  25. Raymond Ng and V. S. Subrahmanian. Stable model semantics for probabilisti deductive databases. In Zbigniew W. Ras and Maria Zemenkova, editors, Proc. of the 6th Int. Sym. on Methodologies for Intelligent Systems (ISMIS-91), number 542 in Lecture Notes in Artificial Intelligence, pages 163–171. Springer-Verlag, 1991. 152, 153, 154

    Google Scholar 

  26. Raymond Ng and V. S. Subrahmanian. Probabilistic logic programming. Information and Computation, 101(2):150–201, 1993. 152, 153

    Article  MathSciNet  Google Scholar 

  27. Raymond Ng and V. S. Subrahmanian. A semantical framework for supporting subjective and conditional probabilities in deductive databases. Journal of Automated Reasoning, 10(3):191–235, 1993. 152, 153

    Article  MATH  MathSciNet  Google Scholar 

  28. Allen nva Gelder, Kenneth A. Ross, and John S. Schlimpf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3):620–650, January 1991. 153, 154, 163

    Article  MATH  Google Scholar 

  29. J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, Los Altos, 1988. 152

    Google Scholar 

  30. T. Przymusinski. Static semantics for normal and disjunctive logic programs. Annals of Mathematics and Artificial Intelligence, 14:323–357, 1995. 153, 159

    Article  MATH  MathSciNet  Google Scholar 

  31. T.C. Przymusinski. Extended stable semantics for normal and disjunctive programs. In D.H.D. Warren and P. Szeredi, editors, Proceedings of the Seventh International Conference on Logic Programming, pages 459–477. MIT Press, 1990. 159

    Google Scholar 

  32. T. C. Przymusinski. Stationary semantics for disjunctive logic programs and deductive databases. In S. Debray and H. Hermenegildo, editors, Logic Programming, Proceedings of the 1990 North American Conference, pages 40–59. MIT Press, 1990. 159

    Google Scholar 

  33. Teodor C. Przymusinski. The well-founded semantics coincides with the three-valued stable semantics. Fundamenta Informaticae, 13(4):445–463, 1990. 153

    MATH  MathSciNet  Google Scholar 

  34. Raymond Reiter. On closed world data bases. In Hervé Gallaire and Jack Minker, editors, Logic and data bases, pages 55–76. Plenum Press, New York, NY, 1978. 153

    Google Scholar 

  35. Ehud Y. Shapiro. Logic programs with uncertainties: A tool for implementing rule-based systems. In Proc. of the 8th Int. Joint Conf. on Artificial Intelligence (IJCAI-83), pages 529–532, 1983. 152

    Google Scholar 

  36. V. S. Subramanian. On the semantics of quantitative logic programs. In Proc. 4th IEEE Symp. on Logic Programming, pages 173–182. Computer Society Press, 1987. 152, 153

    Google Scholar 

  37. M.H. van Emden. Quantitative deduction and its fixpoint theory. Journal of Philosophical Logic, (1):37–53, 1986. 152, 153

    Google Scholar 

  38. Gerd Wagner. Negation in fuzzy and possibilistic logic programs. In T. Martin and F. Arcelli, editors, Logic programming and Soft Computing, pages-. Research Studies Press, 1998. 152, 154

    Google Scholar 

  39. Beat Wüttrich. Probabilistic knowledge bases. IEEE Transactions on Knowledge and Data Engineering, 7(5):691–698, 1995. 152

    Article  Google Scholar 

  40. S. Yablo. Truth and reflection. Journal of Philosophical Logic, 14:297–349, 1985. 161

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Istituto di Elaborazione della Informazione -C.N.R., Via G. Moruzzi, 1, I-56124, Pisa (PI), Italy

    Yann Loyer & Umberto Straccia

Authors
  1. Yann Loyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Umberto Straccia
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematical Informatics, University of Tokyo, Hongo 7-3-1, Bunkyo-Ku, Tokyo, 113-8656, Japan

    Zhenjiang Hu

  2. Department of Informatic Languages and Systems, Universidad Complutense de Madrid, Av. Complutense s/n, 28040, Madrid, Spain

    Mario Rodríguez-Artalejo

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Loyer, Y., Straccia, U. (2002). The Well-Founded Semantics in Normal Logic Programs with Uncertainty. In: Hu, Z., Rodríguez-Artalejo, M. (eds) Functional and Logic Programming. FLOPS 2002. Lecture Notes in Computer Science, vol 2441. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45788-7_9

Download citation

  • DOI: https://doi.org/10.1007/3-540-45788-7_9

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44233-2

  • Online ISBN: 978-3-540-45788-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation