Advertisement

Improving the alternating fixpoint: The transformation approach

  • Ulrich Zukowski
  • Stefan Brass
  • Burkhard Freitag
Regular Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1265)

Abstract

We present a bottom-up algorithm for the computation of the well-founded model of non-disjunctive logic programs which is based on the set of elementary program transformations studied by Brass and Dix [4, 5]. The transformation approach has been introduced in more detail in [7]. In this paper we present a deeper analysis of its complexity and describe an optimized SCC-oriented evaluation. We show that by our method no more work is done than by the alternating fixpoint procedure [23, 24] and that there are examples where our algorithm is significantly superior.

Keywords

Logic Program Logic Programming Conditional Fact Program Component Program Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. Bell, A. Nerode, R. Ng, and V. S. Subrahmanian. Implementing stable semantics by linear programming. In L. M. Pereira and A. Nerode, editors, Logic Programming and Non-monotonic Reasoning, Proc. of the Second Int. Workshop (LPNMR'93), pages 23–42. MIT Press, 1993.Google Scholar
  2. 2.
    S. Brass. Bottom-up query evaluation in extended deductive databases. Habilitationsschrift, Universität Hannover, Fachbereich Mathematik, 1996. http://www.Informatik.uni-hannover.de/∼sb/habil.html.Google Scholar
  3. 3.
    S. Brass. SLDMagic — An improved magic set technique. In B. Novikov and J. W. Schmidt, editors, Advances in Databases and Information Systems — ADBIS'96, 1996.Google Scholar
  4. 4.
    S. Brass and J. Dix. Disjunctive semantics based upon partial and bottom-up evaluation. In L. Sterling, editor, Logic Programming, Proc. of the Twelfth Int. Conf. on Logic Programming (ICLP'95), pages 199–213. MIT Press, 1995.Google Scholar
  5. 5.
    S. Brass and J. Dix. A general approach to bottom-up computation of disjunctive semantics. In J. Dix, L. M. Pereira, and T. C. Przymusinski, editors, Non monotonic Extensions of Logic Programming, number 927 in LNAI, pages 127–155. Springer, 1995.Google Scholar
  6. 6.
    S. Brass and J. Dix. Characterizing D-WPS: Confluence and iterated GCWA. In 5th European Workshop on Logics in AI (JELIA'96), 1996.Google Scholar
  7. 7.
    S. Brass, B. Freitag, and U. Zukowski. Transformation based bottom-up computation of the well-founded model. In J. Dix, L. Pereira, and T. Przymusinski, editors, Non monotonic Extensions of Logic Programming, LNAI 1216, pages 171–201. Springer, Berlin, 1997.Google Scholar
  8. 8.
    F. Bry. Logic programming as constructivism: A formalization and its application to databases. In Proc. of the 8 th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS'89), pages 34–50, 1989.Google Scholar
  9. 9.
    F. Bry. Negation in logic programming: A formalization in constructive logic. In D. Karagiannis, editor, Information Systems and Artificial Intelligence: Integration Aspects, number 474 in LNCS, pages 30–46. Springer, 1990.Google Scholar
  10. 10.
    W. Chen, T. Swift, and D. S. Warren. Efficient top-down computation of queries under the well-founded semantics. Journal of Logic Programming, 24(3): 161–199, 1995.Google Scholar
  11. 11.
    W. Chen and D. S. Warren. Query-evaluation under the well founded semantics. In Proc. of the Twelfth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS'93), pages 168–179, 1993.Google Scholar
  12. 12.
    W. Chen and D. S. Warren. Tabled evaluation with delaying for general logic programs. Journal of the ACM, 43(1):20–74, 1996.Google Scholar
  13. 13.
    P. Cholewiński, V. W. Marek, A. Mikitiuk, and M. Truszczyński. Experimenting with nonmonotonic reasoning. In L. Sterling, editor, Logic Programming, Proc. of the Twelfth Int. Conf. on Logic Programming (ICLP'95), pages 267–281. MIT Press, 1995.Google Scholar
  14. 14.
    L. Degerstedt and U. Nilsson. Magic computation for well-founded semantics. In J. Dix, L. M. Pereira, and T. C. Przymusinski, editors, Nonmonotonic Extensions of Logic Programming, number 927 in LNAI, pages 181–204. Springer, 1995.Google Scholar
  15. 15.
    P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In Proc. North American Conference on Logic Programming (NACLP'89), pages 604–625, 1989.Google Scholar
  16. 16.
    P. M. Dung and K. Kanchansut. A natural semantics of logic programs with negation. In Proc. of the Ninth Conf. on Foundations of Software Technology and Theoretical Computer Science, pages 70–80, 1989.Google Scholar
  17. 17.
    B. Freitag, H. Schütz, and G. Specht. LOLA — a logic language for deductive databases and its implementation. In Proc. 2nd International Symposium on Database Systems for Advanced Applications (DASFAA '91), Tokyo, Japan, April 2–4, 1991, pages 216–225, 1991.Google Scholar
  18. 18.
    M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In R. A. Kowalski and K. A. Bowen, editors, Logic Programming, Proc. of the 5th Int. Conf. and Symp., pages 1070–1080, Cambridge, Mass., 1988. MIT Press.Google Scholar
  19. 19.
    D. B. Kemp, D. Srivastava, and P. J. Stuckey. Bottom-up evaluation and query optimization of well-founded models. Theoretical Computer Science, 146:145–184, 1995.Google Scholar
  20. 20.
    W. Marek and M. Truszczynski. Autoepistemic logic. Journal of the ACM, 38(3):588–619, 1991.Google Scholar
  21. 21.
    K. Sagonas, T. Swift, and D. S. Warren. XSB as an efficient deductive database engine. In R. T. Snodgrass and M. Winslett, editors, Proc. of the 1994 ACM SIG-MOD Int. Conf. on Management of Data (SIGMOD'94), pages 442–453, 1994.Google Scholar
  22. 22.
    V. S. Subrahmanian and C. Zaniolo. Relating stable models and AI planning domains. In L. Sterling, editor, Logic Programming, Proc. of the Twelfth Int. Conf. on Logic Programming (ICLP'95), pages 233–247. MIT Press, 1995.Google Scholar
  23. 23.
    A. Van Gelder. The alternating fixpoint of logic programs with negation. In Proc. of the Eighth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS'89), pages 1–10, 1989.Google Scholar
  24. 24.
    A. Van Gelder. The alternating fixpoint of logic programs with negation. Journal of Computer and System Sciences, 47(1):185–221, 1993.Google Scholar
  25. 25.
    A. Van Gelder, K. Ross, and J. S. Schlipf. Unfounded sets and well-founded semantics for general logic programs. In Proc. of the Seventh ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS'88), pages 221–230, 1988.Google Scholar
  26. 26.
    A. Van Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the Association for Computing Machinary (JACM), 38:620–650, 1991.Google Scholar
  27. 27.
    U. Zukowski and B. Freitag. Adding flexibility to query evaluation for modularly stratified databases. In Proc. of the 1996 Joint International Conference and Symposium on Logic Programming (JICSLP'96). September 2–6, 1996, Bonn, Germany, pages 304–319. MIT Press, 1996.Google Scholar
  28. 28.
    U. Zukowski and B. Freitag. The differential fixpoint of general logic programs. In D. Boulanger, U. Geske, F. Giannotti, and D. Seipel, editors, Proc. of the Workshop DDLP'96 on Deductive Databases and Logic Programming. 4th Workshop in conjunction with JICSLP'96. Bonn, Germany, September 2–6, 1996, volume 295 of GMD-Studien, pages 45–56, St. Augustin, Germany, 1996. GMD.Google Scholar
  29. 29.
    U. Zukowski, B. Freitag, and S. Brass. Transformation-based bottom-up computation of the well-founded model. Technical Report MIP-9620, Universität Passau, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ulrich Zukowski
    • 1
  • Stefan Brass
    • 2
  • Burkhard Freitag
    • 1
  1. 1.Fakultät für Mathematik und InformatikUniversität PassauPassauGermany
  2. 2.Institut für Informatik MarienburgerUniversität HildesheimHildesheimGermany

Personalised recommendations