Skip to main content
Springer Nature Link
Log in

Semantics of disjunctive logic programs and deductive databases

  • Conference paper
  • First Online:
Deductive and Object-Oriented Databases (DOOD 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 566))

Included in the following conference series:

  • 157 Accesses

Abstract

Recently the author introduced the so called stationary semantics which extends the well-founded semantics of normal logic programs to the class of all disjunctive logic programs and deductive databases. The stationary semantics also extends the perfect model semantics defined earlier for stratified disjunctive databases. As a result, the stationary semantics is the only currently known semantics which extends both semantics and is defined for all disjunctive databases.

However, the original definition of stationary semantics was given in terms of 3-valued models and 3-valued theories and therefore seemed to require non-standard, 3-valued logic. In this paper we show, however, that the stationary semantics can be equivalently defined in terms of classical, 2-valued logic, without any reference to 3-valued models. As a byproduct we obtain a simpler and more natural description of the stationary semantics.

For every disjunctive database P we define the so called stationary expansions of P and we show that among all such expansions there is always the smallest one called the stationary completion STAT(P) of P, which, like Clark's Predicate Completion of P, is a first order extension of P providing the appropriate meaning or semantics for the database. We also show that the stationary semantics can be equivalently defined as the iterated minimal model semantics and as the least fixed point of a minimal model operator.

Partialy supported by the National Science Foundation grant #IRI-89-10729, the Army Research Office grant #27079-ML-SAH and the Swedish National Board for Technical Development grant #90-1676.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. K. Apt, H. Blair, and A. Walker. Towards a theory of declarative knowledge. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 89–142, Morgan Kaufmann, Los Altos, CA., 1988.

    Google Scholar 

  2. C. Baral, J. Lobo, and J. Minker. Generalized Disjunctive Well-Founded Semantics for Logic Programs: Declarative Semantics. Research report UMIACS TR 90-39, CS TR 2436, University of Maryland, College Park, Maryland 20742, 1989.

    Google Scholar 

  3. C. Baral, J. Lobo, and J. Minker. Generalized well-founded semantics for logic programs. In 10th International Conference on Automated Deduction, West Germany, 1990.

    Google Scholar 

  4. M. Gelfond. On stratified autoepistemic theories. In Proceedings AAAI-87, pages 207–211, American Association for Artificial Intelligence, Morgan Kaufmann, Los Altos, CA, 1987.

    Google Scholar 

  5. M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In R. Kowalski and K. Bowen, editors, Proceedings of the Fifth Logic Programming Symposium, pages 1070–1080, Association for Logic Programming, MIT Press, Cambridge, Mass., 1988.

    Google Scholar 

  6. M. Gelfond and V. Lifschitz. Logic Programs with Classical Negation. Research report, UT El Paso and Stanford University, 1989.

    Google Scholar 

  7. M. Gelfond, H. Przymusinska, and T. Przymusinski. On the relationship between circumscription and negation as failure. Journal of Artificial Intelligence, 38:75–94, 1989.

    Google Scholar 

  8. J. Horty, R. Thomason, and D. Touretzky. A skeptical theory of inheritance in nonmonotonic semantic nets. In Proceedings AAAI-87, page, American Association for Artificial Intelligence, Morgan Kaufmann, Los Altos, CA, 1987.

    Google Scholar 

  9. M. Keifer, G. Lausen, and J. Wu. Logical Foundations of Object-Oriented and Frame-Based Languages. Research report, SUNY at Stony Brook, 1990.

    Google Scholar 

  10. V. Lifschitz. Computing circumscription. In Proceedings IJCAI-85, pages 121–127, American Association for Artificial Intelligence, Morgan Kaufmann, Los Altos, CA, 1985.

    Google Scholar 

  11. J. McCarthy. Circumscription — a form of non-monotonic reasoning. Journal of Artificial Intelligence, 13:27–39, 1980.

    Google Scholar 

  12. J. Minker. On indefinite data bases and the closed world assumption. In Proc. 6-th Conference on Automated Deduction, pages 292–308, Springer Verlag, New York, 1982.

    Google Scholar 

  13. R.C. Moore. Semantic considerations on non-monotonic logic. Journal of Artificial Intelligence, 25:75–94, 1985.

    Google Scholar 

  14. H. Przymusinska and T. C. Przymusinski. Semantic issues in deductive databases and logic programs. In R. Banerji, editor, Formal Techniques in Artificial Intelligence, pages 321–367, North-Holland, Amsterdam, 1990.

    Google Scholar 

  15. T. C. Przymusinski. On the declarative semantics of stratified deductive databases and logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 193–216, Morgan Kaufmann, Los Altos, CA., 1988.

    Google Scholar 

  16. T. C. Przymusinski. Stationary semantics for disjunctive logic programs and deductive databases. In Proceedings of the North American Logic Programming Conference, Austin, Texas, October 1990, pages 40–59, Association for Logic Programming, MIT Press, Cambridge, Mass., 1990.

    Google Scholar 

  17. T. C. Przymusinski. The well-founded semantics coincides with the three-valued stable semantics. Fundamenta Informaticae, 13(4):445–464, 1990.

    Google Scholar 

  18. T. C. Przymusinski. Autoepistemic logics of closed beliefs and logic programming. In A. Nerode, W. Marek, and V.S. Subrahmanian, editors, Proceedings of the First International Workshop on Logic Programming and Non-monotonic Reasoning, Washington, D.C., July 1991, pages 3–20, MIT Press, Cambridge, Mass., 1991.

    Google Scholar 

  19. T. C. Przymusinski. Stable semantics for disjunctive programs. New Generation Computing Journal, 9, 1991. (October'91 issue. Abstract appeared in: T. C. Przymusinski. Extended stable semantics for normal and disjunctive logic programs. Proceedings of the 7-th International Logic Programming Conference, Jerusalem, pages 459–477, 1990. MIT Press.).

    Google Scholar 

  20. T. C. Przymusinski. Well-founded completions of logic programs. In Proceedings of the Eigth International Logic Programming Conference, Paris, France, pages 726–744, Association for Logic Programming, MIT Press, Cambridge, Mass., 1991.

    Google Scholar 

  21. T. C. Przymusinski and D. S. Warren. Well-founded Semantics: Theory and Implementation. Research report, UT El Paso and SUNY at Stony Brook, 1991. (in preparation).

    Google Scholar 

  22. R. Reiter. On closed-world data bases. In H. Gallaire and J. Minker, editors, Logic and Data Bases, pages 55–76, Plenum Press, New York, 1978.

    Google Scholar 

  23. A. Rajasekar, J. Lobo, and J. Minker. Weak generalized closed world assumption. Journal of Automated Reasoning, 5:293–307, 1989.

    Google Scholar 

  24. K. Ross. The well founded semantics for disjunctive logic programs. In Proceedings of the First International Conference on Deductive and Object Oriented Databases, pages 352–369, 1989.

    Google Scholar 

  25. K. Ross and R. Topor. Inferring negative information from disjunctive databases. Journal of Automated Reasoning, 4:397–424, 1988.

    Google Scholar 

  26. A. Van Gelder. Negation as failure using tight derivations for general logic programs. Journal of Logic Programming, 6(1):109–133, 1989. Preliminary versions appeared in Third IEEE Symp. on Logic Programming (1986), and Foundations of Deductive Databases and Logic Programming, J. Minker, ed., Morgan Kaufmann, 1988.

    Google Scholar 

  27. A. Van Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACMaa, 1990. (to appear). Preliminary abstract appeared in Seventh ACM Symposium on Principles of Database Systems, March 1988, pp. 221–230.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of California at Riverside, USA

    Teodor C. Przymusinski

Authors
  1. Teodor C. Przymusinski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

C. Delobel M. Kifer Y. Masunaga

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Przymusinski, T.C. (1991). Semantics of disjunctive logic programs and deductive databases. In: Delobel, C., Kifer, M., Masunaga, Y. (eds) Deductive and Object-Oriented Databases. DOOD 1991. Lecture Notes in Computer Science, vol 566. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55015-1_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-55015-1_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55015-0

  • Online ISBN: 978-3-540-46646-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics