Advertisement

The differential fixpoint operator with subsumption

  • Gerhard Köstler
  • Werner Kießling
  • Helmut Thöne
  • Ulrich Güntzer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 760)

Abstract

Declarative languages for deductive and object-oriented databases require some high-level mechanism for specifying semantic control knowledge. This paper proposes user-supplied subsumption information as a paradigm to specify desired, prefered or useful deductions at the meta level. For this purpose we augment logic programming by subsumption relations and succeed to extend the classical theorems for least models, fixpoints and bottom-up evaluation accordingly. Moreover, we provide a differential fixpoint operator for efficient query evaluation. This operator discards subsumed tuples on the fly. We also exemplify the ease of use of this programming methodology. In particular, we demonstrate how heuristic AI search procedures can be integrated into logic programming in this way.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hassan Ait-Kaci. Type subsumption as a model of computation. In Proc. Int'l. Workshop on Expert Database Systems. Benjamin Cummings Company, 1985.Google Scholar
  2. 2.
    A. Artale, F. Cesarini, and G. Soda. Introducing knowledge representation techniques in database models. In Trends in Artificial Intelligence, Proc. 2 nd Congr. of the Italian Association for Art. Int., pages 375–384, Palermo, Italy, Oct. 1991. Springer-Verlag.Google Scholar
  3. 3.
    U. S. Chakravarthy, J. Grant, and J. Minker. Logic-based approach to semantic query optimization. ACM Trans. on Database Systems, 15(2):162–207, 1990.Google Scholar
  4. 4.
    Sumit Ganguly, Sergio Greco, and Carlo Zaniolo. Minimum and maximum predicates in logic programming. In Proc. A CM SIGA CT-SIGMOD Symp. on Principles of Database Systems, pages 154–163, Denver, CO, May 1991. ACM Press.Google Scholar
  5. 5.
    Ulrich Güntzer, Werner Kießling, and Rudolf Bayer. On the evaluation of recursion in (deductive) database systems by efficient differential fixpoint iteration. In Proc. IEEE Conf. on Data Eng., pages 120–129, Los Angeles, CA, Feb. 1987.Google Scholar
  6. 6.
    Ulrich Güntzer, Werner Kießling, and Helmut Thöne. New directions for uncertainty reasoning in deductive databases. In Proc. ACM SIGMOD Conf., pages 178–187, Denver, CO, May 1991.Google Scholar
  7. 7.
    Werner Kießling, Gerhard Köstler, and Ulrich Güntzer. Fixpoint evaluation with subsumption for probabilistic uncertainty. In GI-Conference on Datenbanksysteme in Büro, Technik und Wissenschaft, pages 316–333, Braunschweig, Germany, Mar. 1993. Springer-Verlag.Google Scholar
  8. 8.
    Werner Kießling, Helmut Schmidt, Werner Strauß, and Gerhard Dünzinger. DECLARE and SDS: Early efforts to commercialize deductive database technology. VLDB Journal, 1993. submitted.Google Scholar
  9. 9.
    Werner Kießling, Helmut Thöne, and Ulrich Güntzer. Database support for problematic knowledge. In Proc. Int'l. Conf. on Extending Database Technology, pages 421–436, Vienna, Austria, 1992.Google Scholar
  10. 10.
    Michael Kifer and James Wu. A logic for object-oriented logic programming. In Proc. ACM SIGACT-SIGMOD Symp. on Principles of Database Systems, pages 379–393, Philadelphia, PA, Mar. 1989.Google Scholar
  11. 11.
    Byeong Man Kim and Jung Wan Cho. A new subsumption method in the connection graph proof procedure. Theoretical Computer Science, 2:283–309, 1992.Google Scholar
  12. 12.
    Gerhard Köstler, Werner Kießling, Helmut Thöne, and Ulrich Güntzer. The differential fixpoint operator with subsumption. Technical Report TUM-I9315, Fakultät für Informatik, Technische Universität München, Apr. 1993.Google Scholar
  13. 13.
    James B. H. Kwa. BS*: An admissible bidirectional staged heuristic search algorithm. Artificial Intelligence, 38:95–109, 1989.Google Scholar
  14. 14.
    J.W. Lloyd. Foundations of Logic Programming. Springer-Verlag, Berlin, second edition, 1987.Google Scholar
  15. 15.
    Michael J. Maher and Raghu Ramakrishnan. Déjà vu in fixpoints of logic programs. In North American Conference on Logic Programming, pages 963–980, Cleveland, OH, 1989.Google Scholar
  16. 16.
    Inderpal Singh Mumick, Hamid Pirahesh, and Raghu Ramakrishnan. The magic of duplicates and aggregates. In Proc. Int'l. Conf. on Very Large Data Bases, pages 264–277, Brisbane, Australia, Aug. 1990.Google Scholar
  17. 17.
    Nils J. Nilson. Principles of Artificial Intelligence. Tioga Publishing Company, Palo Alto, CA, 1980.Google Scholar
  18. 18.
    Peter F. Patel-Schneider. A four-valued semantics for terminological logics. Artificial Intelligence, 38(3):318–352, 1989.Google Scholar
  19. 19.
    Raghu Ramakrishnan, Divesh Srivastava, and S. Sudarshan. CORAL-Control, Relations and Logic. In Proc. Int'l. Conf. on Very Large Data Bases, pages 238–250, Vancouver, BC, Canada, 1992.Google Scholar
  20. 20.
    Kenneth Ross and Yehoshua Sagiv. Monotonic aggregation in deductive databases. In Proc. ACM SIGACT-SIGMOD Symp. on Principles of Database Systems, pages 114–126, San Diego, CA, Jun. 1992. ACM Press.Google Scholar
  21. 21.
    Helmut Schmidt, Werner Kießling, Ulrich Güntzer, and Rudolf Bayer. Compiling exploratory and goal-directed deduction into sloppy delta-iteration. In Proceedings of the Symposium on Logic Programming, pages 233–243, San Francisco, CA, Sep. 1987.Google Scholar
  22. 22.
    Helmut Schmidt, Werner Kießling, Ulrich Güntzer, and Rudolf Bayer. DBA*: Solving combinatorial problems with deductive databases. In Proc. GI/SI-Conference on Datenbanksysteme in Büro, Technik und Wissenschaft, pages 196–215, Zürich, Switzerland, 1989.Google Scholar
  23. 23.
    A. Tarski. A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math., 5:285–309, 1955.Google Scholar
  24. 24.
    L. Vieille, P. Bayer, and V. Küchenhoff. An overview of the EKS-V1 system. Technical report, ECRC, Munich, Germany, Aug. 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Gerhard Köstler
    • 1
  • Werner Kießling
    • 1
  • Helmut Thöne
    • 2
  • Ulrich Güntzer
    • 2
  1. 1.Lehrstuhl für Informatik IIUniversität AugsburgAugsburgGermany
  2. 2.Wilhelm-Schickard-InstitutUniversität TübingenTübingenGermany

Personalised recommendations