Partial semantics for disjunctive deductive databases

Extended abstract
  • Thomas Eiter
  • Nicola Leone
  • Domenico Saccà
Theoretical Aspects 1
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1134)


We consider in this paper interesting subclasses of partial stable models which reduce the degree of undefinedness, namely M-stable (Maximal-stable) models, which coincide with regular models, preferred extension, and maximal stable classes, and L-stable (Least undefinedstable) models, and we extend them from normal to disjunctive deductive databases.

L-stable models are shown to be the natural relaxation of the notion of total stable model; on the other hand the less strict M-stable models, endowed with a modularity property, may be appealing from the programming and computational point of view. M-stable and L-stable models are also compared with regular models on disjunctive deductive databases. It appears that, unlike on normal deductive databases, M-stable models do not coincide with regular models. Moreover, both M-stable and L-stable models satisfy the CWA principle, while regular models do not.


Logic Program Stable Model Deductive Database Modularity Property Normal Program 
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  1. 1.
    K. Apt and H. Blair. Arithmetic Classification of Perfect Models of Stratified Programs. In Proc. of the Fifth Joint Int'l Conference and Symposium on Logic Programming (JICSLP-88), pp. 766–779. 1988.Google Scholar
  2. 2.
    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
  3. 3.
    J. Dix. Classifying Semantics of Disjunctive Logic Programs. In K. Apt, editor, Proc. JICSLP-92, pp. 798–812. 1992.Google Scholar
  4. 4.
    P. Dung. Negation as Hypotheses: An Abductive Foundation for Logic Programming. In Proc. ICLP-91, pp. 3–17. 1991.Google Scholar
  5. 5.
    T. Eiter, G. Gottlob, and H. Mannila. Adding Disjunction to Datalog. In Proc. PODS '94, pp. 267–278, May 1994.Google Scholar
  6. 6.
    T. Eiter, N. Leone, and D. Saccà. On the Partial Semantics for Disjunctive Deductive Databases. Technical Report CD-TR 95/82, Christian Doppler Lab for Expert Systems, TU Vienna, 1995.Google Scholar
  7. 7.
    M. Fitting. A Kripke-Kleene Semantics for Logic Programs. Journal of Logic Programming, 2(4):295–312, 1985.CrossRefGoogle Scholar
  8. 8.
    M. Gelfond and V. Lifschitz. The Stable Model Semantics for Logic Programming. In Proc. Fifth Intl Conference and Symposium, pp. 1070–1080. 1988.Google Scholar
  9. 9.
    A. Kakas and P. Mancarella. Preferred Extensions are Partial Stable Models. Journal of Logic Programming, 14:341–348, 1992.CrossRefGoogle Scholar
  10. 10.
    V. Lifschitz and H. Turner. Splitting a Logic Program. In Proc. ICLP-94, pp. 23–38, MIT-Press, 1994.Google Scholar
  11. 11.
    J. Minker. On Indefinite Data Bases and the Closed World Assumption. In Proc. CADE '82, pp. 292–308, LNCS 138. Springer, 1982.Google Scholar
  12. 12.
    T. Przymusinski. Stable Semantics for Disjunctive Programs. New Generation Computing, 9:401–424, 1991.Google Scholar
  13. 13.
    R. Reiter. On Closed-World Databases. In H. Gallaire and J. Minker, editors, Logic and Data Bases, pp. 55–76. Plenum Press, New York, 1978.Google Scholar
  14. 14.
    K. Ross. Modular Stratification and Magic Sets for Datalog Programs with Negation. Journal of the ACM, 41(6):1216–1267, 1994.CrossRefGoogle Scholar
  15. 15.
    D. Saccá. The Expressive Powers of Stable Models for Bound and Unbound DAT-ALOG Queries. Journal of Computer and System Sciences, 1996. To appear.Google Scholar
  16. 16.
    J. Schlipf. The Expressive Powers of Logic Programming Semantics. Journal of Computer and System Sciences, 51(1):64–86, 1995.CrossRefGoogle Scholar
  17. 17.
    J. D. Ullman. Principles of Database and Knowledge Base Systems. Computer Science Press, 1988.Google Scholar
  18. 18.
    A. van Gelder, K. Ross, and J. Schlipf. The Well-Founded Semantics for General Logic Programs. Journal of the ACM, 38(3):620–650, 1991.Google Scholar
  19. 19.
    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.CrossRefGoogle Scholar
  20. 20.
    J.-H. You and L. Yuan. On the Equivalence of Semantics for Normal Logic Programming. Journal of Logic Programming, 22(3):211–222, 1995.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Thomas Eiter
    • 1
  • Nicola Leone
    • 1
  • Domenico Saccà
    • 2
  1. 1.Christian Doppler Lab for Expert Systems Institut für InformationssystemeTU WienWienAustria
  2. 2.DEIS-UNICALUniversità della CalabriaRendeItaly

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