Skip to main content
SpringerLink
Log in
Book cover

International Conference on Logic Programming and Nonmonotonic Reasoning

LPNMR 1999: Logic Programming and Nonmonotonic Reasoning pp 290–304Cite as

Extending Disjunctive Logic Programming by T-norms

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1730))

Abstract

This paper proposes a new knowledge representation language, called QDLP, which extends DLP to deal with uncertain values. A certainty degree interval (a subinterval of [0, 1] is assigned to each (quantitative) rule. Triangular norms (T-norms) are employed to define calculi for propagating uncertainty information from the premises to the conclusion of a quantitative rule. Negation is considered and the concept of stable model is extended to QDLP. Different T-norms induce different semantics for one given quantitative program. In this sense, QDLP is parameterized and each choice of a T-norm induces a different QDLP language. Each T-norm is eligible for events with determinate relationships (e.g., independence, exclusiveness) between them. Since there are infinitely many T-norms, it turns out that there is a family of infinitely many QDLP languages.This family is carefully studied and the set of QDLP languages which generalize traditional DLP is precisely singled out. Finally, the complexity of the main decisional problems arising in the context of QDLP (i.e., Model Checking, Stable Model Checking, Consistency, and Brave Reasoning) is analyzed. It is shown that the complexity of the relevant fragments of QDLP coincides exactly with the complexity of DLP. That is, reasoning with uncertain values is more general and not harder than reasoning with boolean values.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K.R. Apt, H.A. Blair, and A. Walker. Towards a Theory of Declarative Knowledge. Foundations of Deductive Databases and Logic Programming, Minker, J. (ed.), Morgan Kaufmann, Los Altos, 1987.

    Google Scholar 

  2. F. Bacchus. Representing and Reasoning with Probabilistic Knowledge. Research Report CS-88-31, University of Waterloo, 1988.

    Google Scholar 

  3. Baral, C., Gelfond, M. Logic Programming and Knowledge Representation. Journal of Logic Programming, Vol. 19/20, May/July, pp. 73–148, 1994. 302 C. Mateis

    Article  Google Scholar 

  4. R. Ben-Eliyahu and R. Dechter. Propositional Semantics for Disjunctive Logic Programs. Annals of Mathematics and Artificial Intelligence, 12:53–87, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  5. R. Ben-Eliyahu and L. Palopoli. Reasoning with Minimal Models: Efficient Algorithms and Applications. In Proc. KR-94, pp. 39–50, 1994.

    Google Scholar 

  6. H.A. Blair and V.S. Subrahmanian. Paraconsistent Logic Programming. Theoretical Computer Science, 68, pp. 35–54, 1987.

    MathSciNet  Google Scholar 

  7. P. Bonissone. Summarizing and Propagating Uncertain Information with Triangular Norms. International Journal of Approximate Reasoning, 1:71–101,1987.

    Article  MathSciNet  Google Scholar 

  8. P.R. Cohen and M.R. Grinberg. A Framework for Heuristic Reasoning about Uncertainty. In Proc. IJCAI’ 83, pp. 355–357, Karlsruhe, Germany, 1983.

    Google Scholar 

  9. P.R. Cohen and M.R. Grinberg. A Theory of Heuristics Reasoning about Uncertainty. AI Magazine, 4(2):17–23, 1983.

    Google Scholar 

  10. A.P. Dempster. A Generalization of Bayesian Inference. J. of the Royal Statistical Society, Series B, 30, pp. 205–247, 1968.

    MathSciNet  Google Scholar 

  11. J. Dix. Semantics of Logic Programs: Their Intuitions and Formal Properties. An Overview. In Logic, Action and Information, pp. 241–329. DeGruyter, 1995.

    Google Scholar 

  12. J. Doyle. Methodological Simplicity in Expert System Construction: the Case of Judgements and Reasoned Assumptions. AI Magazine, 4(2):39–43, 1983.

    MathSciNet  Google Scholar 

  13. T. Eiter, G. Gottlob, and H. Mannila. Disjunctive Datalog. ACM Transaction on Database System, 22(3):364–417, September 1997.

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  15. M.C. Fitting. Bilattices and the Semantics of Logic Programming. J. Logic Programming, 11, pp. 91–116, 1991.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  17. M. Ishizuka. Inference Methods Based on Extended Dempster-Shafer Theory for Problems with Uncertainty/Fuzziness. New Generation Computing, 1, 2, pp. 159–168, 1983.

    Google Scholar 

  18. M. Kifer and A. Li. On the Semantics of Rule-Based Expert Systems with Uncertainty. In 2-nd International Conference on Database Theory, Springer Verlag LNCS 326, pp. 102–117, 1988.

    Google Scholar 

  19. M. Kifer and V.S. Subrahmanian. Theory of the Generalized Annotated Logic Programming and its Applications. J. Logic Programming, 12, pp. 335–367, 1992.

    Article  MathSciNet  Google Scholar 

  20. L.V.S. Lakshmanan, N. Leone, R. Ross, and V.S. Subrahmanian. ProbView: A Flexible Probabilistic Database System. ACM Transaction on Database Systems, 22, 3, pp. 419–469, 1997.

    Article  Google Scholar 

  21. J.W. Lloyd. Foundations of Logic Programming. Springer-Verlag, 1987.

    Google Scholar 

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

    Google Scholar 

  23. C. Mateis. A Quantitative Extension of Disjunctive Logic Programming. Technical Report, available on the web as: http://www.dbai.tuwien.ac.at/staff/mateis/gz/qdlp.ps.

  24. R.T. Ng and V.S. Subrahmanian. Probabilistic Logic Programming. Information and Computation, 101:150–201, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  25. R.T. Ng and V.S. Subrahmanian. Empirical Probabilities in Monadic Deductive Databases. In Proc. Eighth Conf. Uncertainty in AI, pp. 215–222, Stanford, 1992.

    Google Scholar 

  26. R.T. Ng and V.S. Subrahmanian. A Semantical Framework for Supporting Subjective and Conditional Probabilities in Deductive Databases. J. of Automated Reasoning, 10, 2, pp. 191–235, 1993.

    Article  MathSciNet  Google Scholar 

  27. R.T. Ng and V.S. Subrahmanian. Stable Semantics for Probabilistic Deductive Databases. Information and Computation, 110:42–83, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  28. R.T. Ng and V.S. Subrahmanian. Non-monotonic Negation in Probabilistic Deductive Databases. In Proc. 7-th Conf. Uncertainty in AI, pp. 249–256, Los Angeles, 1991.

    Google Scholar 

  29. N.J. Nilsson. Probabilistic Logic. Articial Intelligence, vol. 28, pp. 71–87, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  30. J. Pearl. Probabilistic Reasoning in Intelligent Systems-Networks of Plausible Inference. Morgan Kaufmann, 1988.

    Google Scholar 

  31. B. Schweizer and A. Sklar. Associative Functions and Abstract Semi-Groups. Publicationes Mathematicae Debrecen, 10:69–81, 1963.

    MathSciNet  Google Scholar 

  32. G. Shafer. A Mathematical Theory of Evidence. Princeton University Press, 1976.

    Google Scholar 

  33. E. Shapiro. Logic Programs with Uncertainties: A Tool for Implementing Expert Systems. In Proc. IJCAI’ 83, pp. 529–532, 1983.

    Google Scholar 

  34. M.H. van Emden. Quantitative Deduction and its Fixpoint Theory. The Journal of Logic Programming, 1:37–53, 1986.

    Article  Google Scholar 

  35. L.A. Zadeh. Fuzzy Sets. Inform. and Control, 8:338–353, 1965.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Information Systems Department, TU Vienna, A-1040, Vienna, Austria

    Cristinel Mateis

Authors
  1. Cristinel Mateis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at El Paso, El Paso, TX, 79916, USA

    Michael Gelfond

  2. Institut für Informationssysteme 184/2, Technische Universität Wien, Favoritenstrβe 9-11, A-1040, Vienna, Austria

    Nicola Leone  & Gerald Pfeifer  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mateis, C. (1999). Extending Disjunctive Logic Programming by T-norms. In: Gelfond, M., Leone, N., Pfeifer, G. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 1999. Lecture Notes in Computer Science(), vol 1730. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46767-X_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-46767-X_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66749-0

  • Online ISBN: 978-3-540-46767-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation