Modeling uncertainty in deductive databases

  • Laks V. S. Lakshmanan
  • Fereidoon Sadri
Integration of Databases and Expert Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 856)


Information Source Tracking (IST) method has been developed recently for the modeling and manipulation of uncertain and inaccurate data in relational databases. In this paper we extend the IST method to deductive databases. We show that positive uncertain databases, i.e. IST-based deductive databases with only positive literals in the heads and the bodies of the rules, enjoy a least model/least fixpoint semantics. Query processing in this model is studied next. We extend the top-down and bottom-up evaluation techniques of logic programming and deductive databases to our model. Finally, we study negation for uncertain databases, concentrating on stratified uncertain databases.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. R. Apt, “Introduction to Logic Programming.” Technical Report CS-R8741, September 1987, Centre for Mathematics and Computer Science, Computer Science/Department of Software Technology, The Netherlands.Google Scholar
  2. 2.
    K. R. Apt, H. A. Blair, and A. Walker, “Towards a Theory of Declarative Knowledge.” in Foundations of Deductive Databases and Logic Programming, J. Minker Ed., Morgan Kaufmann, 1988, pp 89–148.Google Scholar
  3. 3.
    F. Bancilhon, D. Maier, Y. Sagiv, and J.D. Ullman, “Magic Sets and Other Strange Ways to Implement Logic Programs.” Proceedings of the 1986 ACM Symposium on Principles of Database Systems, pp 1–15.Google Scholar
  4. 4.
    D. Barbara, H. Garcia-Molina, and D. Porter, “The Management of Probabilistic Data.” IEEE Transactions on Knowledge and Data Engineering, Vol. 4, No. 5, October 1992, pp 487–502.CrossRefGoogle Scholar
  5. 5.
    M. Kifer, and A. Li, “On the Semantics of Rule-Based Expert Systems with Uncertainty. ” Proceedings of the 2nd International Conference on Database Theory, Springer Verlag LNCS 326, M. Gyssens, J. Paredaens, and D. Van Gucht, eds., 1988, pp 102–117.Google Scholar
  6. 6.
    V. S. Lakshmanan, “Query Processing with Null Values: How Complex is Completeness?” Proc. Int'l Conf. Foundations of Software Technology and Theoretical Computer Science, Bangalore, December 1989, Lecture Notes in Computer Science, Vol. 405, pp 204–222, Springer, 1989.Google Scholar
  7. 7.
    Suk Kyoon Lee, “Imprecise and Uncertain Information in Databases: An Evidential Approach.” Proceedings of the 1992 IEEE International Conference on Data Engineering, pp 614–621.Google Scholar
  8. 8.
    K-C. Liu, and R. Sunderraman, “Indefinite and Maybe Information in Relational Databases.” ACM TODS, Vol. 15, No. 1, March 1990, pp 1–39.Google Scholar
  9. 9.
    K-C. Liu, and R. Sunderraman, “A Generalized Relational Model for Indefinite and Maybe Information.” IEEE Transactions on Knowledge and Data Engineering, Vol. 3, No. 1, March 1991, pp 65–77.Google Scholar
  10. 10.
    J. W. Lloyd, Foundations of Logic Programming, Springer-Verlag, 1984.Google Scholar
  11. 11.
    R. Ng, and V. S. Subrahmanian, “A Semantical Framework for Supporting Subjective and Conditional Probabilities in Deductive Databases.” Tech. Rep. No. CS-TR-2563, Dept. of Computer Science, University of Maryland, November 1990.Google Scholar
  12. 12.
    N. J. Nilsson, “Probabilistic Logic.” Artificial Intelligence, Vol. 28, 1986, pp 71–87.CrossRefGoogle Scholar
  13. 13.
    R. Ramakrishnan, “Magic Templates: A Spellbinding Approach to Logic Programs.” Proc. Fifth Int'l Symp. on Logic Programming, 1988, pp 140–159.Google Scholar
  14. 14.
    F. Sadri “Reliability of Answers to queries in Relational Databases.” IEEE Transactions on Knowledge and Data Engineering, Vol. 3, No. 2, June 91, pp 245–251.Google Scholar
  15. 15.
    F. Sadri “Modeling Uncertainty in Databases.” Proceedings of the 1991 IEEE International Conference on Data Engineering, pp 122–131.Google Scholar
  16. 16.
    F. Sadri, “Information Source Tracking Method: Efficiency Issues.” Manuscript. December 1992. Submitted for publication.Google Scholar
  17. 17.
    F. Sadri “Integrity Constraints in the Information Source Tracking Method.” To appear in IEEE Transactions on Knowledge and Data Engineering.Google Scholar
  18. 18.
    A. Silberschatz, M. Stonebraker, and J. D. Ullman, “Database Systems: Achievements and Opportunities.” Comm. ACM, Vol. 34, No. 10, October 1991, pp 110–120.Google Scholar
  19. 19.
    J. D. Ullman, Principles of Database and Knowledge-Base Systems, Volume II, Computer Science Press, 1989.Google Scholar
  20. 20.
    J. D. Ullman, “Bottom-up Beats Top-down for Datalog.” Proceedings of the 1989 ACM Symposium on Principles of Database Systems, pp 140–149.Google Scholar
  21. 21.
    M. H. Van Emden, “Quantitative Deduction and its Fixpoint Theory.” Journal of Logic Programming, Vol. 4, No. 1, 1986, pp 37–53.Google Scholar
  22. 22.
    M. H. Van Emden, and R. A. Kowalski, “The Semantics of Predicate Logic as a Programming Language.” Journal of the ACM, Vol. 23, No. 4, October 1976, pp 733–742.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Laks V. S. Lakshmanan
    • 1
  • Fereidoon Sadri
    • 1
  1. 1.Concordia UniversityMontrealCanada

Personalised recommendations