Order and Negation as Failure

  • Davy Van Nieuwenborgh
  • Dirk Vermeir
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2916)


We equip ordered logic programs with negation as failure, using a simple generalization of the preferred answer set semantics for ordered programs. This extension supports a convenient formulation of certain problems, which is illustrated by means of an intuitive simulation of logic programming with ordered disjunction. The simulation also supports a broader application of “ordered disjunction”, handling problems that would be cumbersome to express using ordered disjunction logic programs.

Interestingly, allowing negation as failure in ordered logic programs does not yield any extra computational power: the combination of negation as failure and order can be simulated using order (and true negation) alone.


Logic Program Logic Programming Simple Program Disjunctive Program Stable Model Semantic 
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.


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  1. 1.
    Brewka, G.: Logic programming with ordered disjunction. In: Proc. of the 18th AAAI Conf., pp. 100–105. AAAI Press, Menlo Park (2002)Google Scholar
  2. 2.
    Brewka, G., Benferhat, S., Le Berre, D.: Qualitative choice logic. In: Proc. of the 8th Intl. Conf. on Knowledge Representation and Reasoning, pp. 158–169. Morgan Kaufmann, San Francisco (2002)Google Scholar
  3. 3.
    Brewka, G., Eiter, T.: Preferred answer sets for extended logic programs. Artificial Intelligence 109(1-2), 297–356 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Brewka, G., Niemela, I., Syrjanen, T.: Implementing ordered disjunction using answer set solvers for normal programs. In: Flesca et al. [10], pp. 444–455Google Scholar
  5. 5.
    Buccafurri, F., Faber, W., Leone, N.: Disjunctive logic programs with inheritance. In: De Schreye, D. (ed.) Proc. of the Intl. Conf. on Logic Programming, pp. 79–93. MIT Press, Cambridge (1999)Google Scholar
  6. 6.
    Buccafurri, F., Leone, N., Rullo, P.: Disjunctive ordered logic: Semantics and expressiveness. In: Cohn, A., et al. (eds.) Proc. of the 6th Intl. Conf. on Principles of Knowledge Representation and Reasoning, pp. 418–431. Morgan Kaufmann, San Francisco (1998)Google Scholar
  7. 7.
    Clark, K.L.: Negation as failure. In: Gallaire, H., Minker, J. (eds.) Logic and Data Bases, pp. 293–322. Plenum Press, New York (1978)Google Scholar
  8. 8.
    De Vos, M., Vermeir, D.: Dynamically ordered probabilistic choice logic programming. In: Kapoor, S., Prasad, S. (eds.) FST TCS 2000. LNCS, vol. 1974, pp. 227–239. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  9. 9.
    Eiter, T., Gottlob, G., Leone, N.: Abduction from logic programs: Semantics and complexity. Theoretical Computer Science 189(1-2), 129–177 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.): JELIA 2002. LNCS (LNAI), vol. 2424. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  11. 11.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R., et al. (eds.) Proc. of the 5th Intl. Conf. on Logic Programming, pp. 1070–1080. MIT Press, Cambridge (1988)Google Scholar
  12. 12.
    Inoue, K., Sakama, C.: On positive occurrences of negation as failure. In: Doyle, J., et al. (ed.) Proc. of the 4th Intl. Conf. on Principles of Knowledge Representation and Reasoning, pp. 293–304. Morgan Kaufmann, San Francisco (1994)Google Scholar
  13. 13.
    Inoue, K., Sakama, C.: A fixpoint characterization of abductive logic programs. Journal of Logic Programming 27(2), 107–136 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Inoue, K., Sakama, C.: Negation as failure in the head. Journal of Logic Programming 35(1), 39–78 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Kakas, C., Kowalski, R.A., Toni, F.: Abductive logic programming. Journal of Logic and Computation 2(6), 719–770 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Kowalski, R.A., Sadri, F.: Logic programs with exceptions. In: Warren, D.H.D., Szeredi, P. (eds.) Proc. of the 7th Intl. Conf. on Logic Programming, pp. 598–613. The MIT Press, Cambridge (1990)Google Scholar
  17. 17.
    Laenens, E., Vermeir, D.: A fixpoint semantics of ordered logic. Journal of Logic and Computation 1(2), 159–185 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Laenens, E., Vermeir, D.: Assumption-free semantics for ordered logic programs: On the relationship between well-founded and stable partial models. Journal of Logic and Computation 2(2), 133–172 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Leone, N., Rullo, P., Scarcello, F.: Disjunctive stable models: Unfounded sets, fixpoint semantics, and computation. Information and Computation 135(2), 69–112 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Lifschitz, V.: Answer set programming and plan generation. Journal of Artificial Intelligence 138(1-2), 39–54 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Przymusinski, T.C.: Stable semantics for disjunctive programs. New Generation Computing 9(3-4), 401–424 (1991)CrossRefGoogle Scholar
  22. 22.
    Reiter, R.: A theory of diagnosis from first principles. Artificial Intelligence 32(1), 57–95 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Sakama, C., Inoue, K.: An alternative approach to the semantics of disjunctive logic programs and deductive databases. Journal of Automated Reasoning 13(1), 145–172 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Sakama, C., Inoue, K.: Representing priorities in logic programs. In: Maher, M.J. (ed.) Proc. of the Intl. Conf. on Logic Programming, pp. 82–96. MIT Press, Cambridge (1996)Google Scholar
  25. 25.
    van Gelder, A., Ross, K.A., Schlipf, J.S.: Unfounded sets and well-founded semantics for general logic programs. In: Proc. of the 7th PODS Symposium, pp. 221–230. ACM Press, New York (1988)Google Scholar
  26. 26.
    Van Nieuwenborgh, D., Vermeir, D.: Order and negation as failure. Technical report, Vrije Universiteit Brussel, Dept. of Computer Science (2003)Google Scholar
  27. 27.
    Van Nieuwenborgh, D., Vermeir, D.: Preferred answer sets for ordered logic programs. In: Flesca et al. [10], pp. 432–443Google Scholar
  28. 28.
    Wang, K., Zhou, L., Lin, F.: Alternating fixpoint theory for logic programs with priority. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 164–178. Springer, Heidelberg (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Davy Van Nieuwenborgh
    • 1
  • Dirk Vermeir
    • 1
  1. 1.Dept. of Computer ScienceVrije Universiteit Brussel, VUB 

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