Learning non-monotonic logic programs: Learning exceptions

  • Yannis Dimopoulos
  • Antonis Kakas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 912)


In this paper we present a framework for learning non-monotonic logic programs. The method is parametric on a classical learning algorithm whose generated rules are to be understood as default rules. This means that these rules must be tolerant to the negative information by allowing for the possibility of exceptions. The same classical algorithm is then used to learn recursively these exceptions.

We prove that the non-monotonic learning algorithm that realizes these ideas converges asymptotically to the concept to be learned. We also discuss various general issues concerning the problem of learning nonmonotonic theories in the proposed framework.


  1. 1.
    M. Bain and S. Muggleton, Non-monotonic learning. In: J.E. Hayes-Michie and E. Tyugu, eds., Machine Intelligence 12. Oxford University Press, 1990Google Scholar
  2. 2.
    K.L. Clark. Negation as failure. In Logic and databases, Gallaire and Minker, eds., Plenum Press, 1978.Google Scholar
  3. 3.
    J. Cussens, A. Hunter and A. Srinivasan. Generating explicit ordering for nonmonotonic logics. Proc. of AAAI-93.Google Scholar
  4. 4.
    L. De Raedt. Interactive Theory Revision: an Inductive Logic Programming Approach. Academic Press, 1992.Google Scholar
  5. 5.
    L. De Raedt and M. Bruynooghe. On negation and three-valued logic in interactive concept learning. Proc. of the 9th European Conference on AI, ECAI-90, 207–212, 1990.Google Scholar
  6. 6.
    M. Gelfond and V. Lifschitz. The stable model semantics for logic programs. Proc. of the 5th International Conference and Symposium on Logic Programming, 1070–1080, MIT Press, 1990.Google Scholar
  7. 7.
    E.M. Gold. Language identification in the limit. Information and Control, 10:447–474, 1967.Google Scholar
  8. 8.
    A. Kakas, P. Mancarela and P. M. Dung. The acceptability semantics for logic programs. Proc. of 11th Inter. Conference on Logic Programming, ICLP-94, 504–519, MIT Press, 1994.Google Scholar
  9. 9.
    J-U. Kietz and S. Dzeroski. Inductive logic programming and learnability. SIGART Newsletters, 5(1), 1994.Google Scholar
  10. 10.
    N. Lavrac and S. Dzeroski. Inductive Logic Programming: Techniques and Applications. Ellis Horwood, 1994.Google Scholar
  11. 11.
    C. Ling. Non-Monotonic specialization. Proc. of the Inductive Logic Programming Workshop, ILP-91, 1991.Google Scholar
  12. 12.
    S. Muggleton and W. Buntime. Machine invention of first order predicates by inverting resolution. Proc. of the 5th Inter. Conference on Machine Learning, 339–352, Kaufmann, 1988.Google Scholar
  13. 13.
    S. Muggleton. Inductive logic programming. New Generation Computing, 8, 295–318, 1991.Google Scholar
  14. 14.
    S. Muggleton and L. De Raedt. Inductive logic programming: Theory and methods. submitted.Google Scholar
  15. 15.
    T. Przymusinski, On the declarative and procedural semantics of logic programs. Journal of Automated Reasoning, 5, 167–205, 1989.Google Scholar
  16. 16.
    A. Srinivasan, S. Muggleton and M. Bain. Distinguishing exceptions from noise in non-monotonic learning. Proc. of the International Workshop on Inductive Logic Programming, S. Muggleton and K. Furukawa, Japan, 1992.Google Scholar
  17. 17.
    S. Wrobel. On the proper definition of minimality in specialization and theory revision. Proc. of the European Conference on Machine Learning, ECML-93, Vienna, 1993, LNAI 667, Springer Verlag.Google Scholar
  18. 18.
    A. Van Gelder, K. A. Ross and J. S. Schlipf. Unfounded sets and well-founded semantics for general logic programs. Proc. of the 7th Symposium on Principles of Database Systems, PODS-88, 221–230, ACM Press, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Yannis Dimopoulos
    • 1
  • Antonis Kakas
    • 1
  1. 1.Department of Computer ScienceUniversity of CyprusNicosiaCyprus

Personalised recommendations