The expressive power of partial models for disjunctive deductive databases

Extended abstract
  • T. Eiter
  • N. Leone
  • D. Saccà
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1154)


We investigate the expressive power of partial model semantics for disjunctive deductive databases. In particular, partial stable, regular model, maximal stable (M-stable), and least undefined stable (L-stable) semantics for function-free disjunctive logic programs are considered, for which the expressiveness of queries based on possibility and certainty inference is determined. The analysis pays particular attention to the impact of syntactical restrictions on programs in the form of limited use of disjunction and negation. It appears that the considered semantics capture complexity classes at the lower end of the polynomial hierarchy. In particular, L-stable semantics has the highest expressive power (Σsk3/P resp. Πsk3/P). An interesting result in this course is that, in contrast with total stable models, negation is for partial stable models more expressive than disjunction.


Logic Program Stable Model Partial Model Expressive Power Deductive Database 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Abiteboul, E. Simon, and V. Vianu. Non-Deterministic Languages to Express Deterministic Transformations. In Proc. PODS-90, pp. 218–229, 1990.Google Scholar
  2. 2.
    S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1995.Google Scholar
  3. 3.
    S. Abiteboul, P. Kanellakis, and G. Grahne. On the Representation and Querying of Sets of Possible Worlds. Theoretical Computer Science, 78:159–187, 1991.Google Scholar
  4. 4.
    C. Baral and V. Subrahmanian. Stable and Extension Class Theory for Logic Programs and Default Logic. Journal of Automated Reasoning, 8:345–366, 1992.Google Scholar
  5. 5.
    R. Ben-Eliyahu and R. Dechter. Propositional Semantics for Disjunctive Logic Programs. Annals of Mathematics and Artificial Intelligence, 12:53–87, 1994.Google Scholar
  6. 6.
    R. Ben-Eliyahu and L. Palopoli. Reasoning with Minimal Models: Efficient Algorithms and Applications. In Proc. KR-94, pp. 39–50, 1994.Google Scholar
  7. 7.
    S. Ceri, G. Gottlob, and L. Tanca. Logic Programming and Databases. 1990.Google Scholar
  8. 8.
    A. Chandra and D. Harel. Structure and Complexity of Relational Queries. Journal of Computer and System Sciences, 25:99–128, 1982.Google Scholar
  9. 9.
    A. Dawar. A Restricted Second Order Logic for Finite Structures. In D. Leivant, editor, Proc. Intl Workshop LCC '94, LNCS 960, 1995.Google Scholar
  10. 10.
    P. Dung. Negation as Hypotheses: An Abductive Foundation for Logic Programming. In Proc. ICLP-91, pp. 3–17. MIT Press, 1991.Google Scholar
  11. 11.
    T. Eiter and G. Gottlob. On the Computational Cost of Disjunctive Logic Programming: Prepositional Case. Annals of Mathematics and Artificial Intelligence, 15(3/4):289–323, 1995.Google Scholar
  12. 12.
    T. Eiter, G. Gottlob, and H. Mannila. Adding Disjunction to Datalog. In Proc. PODS-94, pp. 267–278, May 1994.Google Scholar
  13. 13.
    T. Eiter, N. Leone, and D. Saccà. On the Partial Semantics for Disjunctive Deductive Databases. Annals of Mathematics and Artificial Intelligence, to appear, CD-TR 95/82, CD-Lab for Expert Systems, TU Vienna, August 1995.Google Scholar
  14. 14.
    T. Eiter, N. Leone, and D. Saccà. Expressive Power and Complexity of Partial Models for Disjunctive Deductive Databases. Technical Report CD-TR 95/83, Christian Doppler Laboratory for Expert Systems, TU Vienna, August 1995.Google Scholar
  15. 15.
    D. W. Etherington. Reasoning with Incomplete Information. Morgan Kaufmann Publishers, Inc., Los Altos, 1988.Google Scholar
  16. 16.
    R. Fagin. Generalized First-Order Spectra and Polynomial-Time Recognizable Sets. In R. M. Karp, editor, Complexity of Computation, pp. 43–74. AMS, 1974.Google Scholar
  17. 17.
    M. Gelfond and V. Lifschitz. The Stable Model Semantics for Logic Programming. In Logic Programming: Proc. Fifth Intl Conference and Symposium, pp. 1070–1080, MIT Press, 1988.Google Scholar
  18. 18.
    G. Gottlob. Complexity and Expressive Power of Disjunctive Logic Programming. In M. Bruynooghe, editor, Proc. ILPS-94, pp. 23–42, Ithaca NY, 1994. MIT Press.Google Scholar
  19. 19.
    G. Grahne. The Problem of Incomplete Information in Relational Databases, LNCS 554, 1991.Google Scholar
  20. 20.
    A. Kakas and P. Mancarella. Preferred Extensions are Partial Stable Models. Journal of Logic Programming, 14:341–348, 1992.Google Scholar
  21. 21.
    P. Kanellakis. Elements of Relational Database Theory. In J. van Leeuwen, editor, Handbook of TCS (B), 1990.Google Scholar
  22. 22.
    P. Kolaitis. The Expressive Power of Stratified Logic Programs. Information and Computation, 90:50–66, 1991.Google Scholar
  23. 23.
    T. Przymusinski. Stable Semantics for Disjunctive Programs. New Generation Computing, 9:401–424, 1991.Google Scholar
  24. 24.
    D. Saccá. The Expressive Powers of Stable Models for Bound and Unbound DATALOG Queries. Journal of Computer and System Sciences. To appear.Google Scholar
  25. 25.
    D. Saccá, C. Zaniolo. Deterministic and Non-Deterministic Stable Models, submitted for publication to Journal of Logic and Computation, T.R. ISI-CNR, 1996.Google Scholar
  26. 26.
    D. Saccá, C. Zaniolo. Stable Models and Nondeterminism in Logic Programs with Negation. Proc. ACM PODS, 1990.Google Scholar
  27. 27.
    J. Schlipf. Complexity and Undecidability Results in Logic Programming. Annals of Mathematics and Artificial Intelligence, 15(3/4):257–288, 1995.Google Scholar
  28. 28.
    L. J. Stockmeyer. The Polynomial-Time Hierarchy. Theoretical Computer Science, 3:1–22, 1977.Google Scholar
  29. 29.
    J. D. Ullman. Principles of Database and Knowledge Base Systems. CS Press, 1989.Google Scholar
  30. 30.
    M. Vardi. Complexity of relational query languages. In Proc. 14th ACM STOC, pp. 137–146, 1982.Google Scholar
  31. 31.
    J.-H. You and L. Yuan. A Three-Valued Semantics for Deductive Databases and Logic Programs. Journal of Computer and System Sciences, 49:334–361, 1994.Google Scholar
  32. 32.
    J.-H. You and L. Yuan. On the Equivalence of Semantics for Normal Logic Programming. Journal of Logic Programming, 22(3):211–222, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • T. Eiter
    • 1
  • N. Leone
    • 1
    • 2
  • D. Saccà
    • 3
  1. 1.Christian Doppler Lab for Expert Systems Institut für InformationssystemeTU WienWienAustria
  2. 2.ISI-CNR c/o DEIS-UNICALItaly
  3. 3.DEIS-UNICALUniversità della CalabriaRendeItaly

Personalised recommendations