Some Properties of Inverse Resolution in Normal Logic Programs

  • Chiaki Sakama
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1634)


This paper studies the properties of inverse resolution in normal logic programs. The V-operators are known as operations for inductive generalization in definite logic programs. In the presence of negation as failure in a program, however, the V-operators do not work as generalization operations in general and often make a consistent program inconsistent. Moreover, they may destroy the syntactic structure of logic programs such as acyclicity and local stratification. On the procedural side, unrestricted application of the V-operators may lose answers computed in the original program and make queries flounder. We provide sufficient conditions for the V-operators to avoid these problems.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. R. Apt, H. A. Blair, and A. Walker. Towards a theory of declarative knowledge. In: Foundations of Deductive Databases and Logic Programming (J. Minker ed.), Morgan Kaufmann, pp. 89–148, 1988.Google Scholar
  2. 2.
    K. R. Apt and M. Bezem. Acyclic programs. New Generation Computing 9:335–363, 1991.CrossRefGoogle Scholar
  3. 3.
    M. Bain and S. Muggleton. Non-monotonic learning. In: [14], pp. 145–161.Google Scholar
  4. 4.
    M. Bain. Experiments in non-monotonic first-order induction. In: [14], pp. 423–436.Google Scholar
  5. 5.
    R. B. Banerji. Learning theoretical terms. In: [14], pp. 93–112.Google Scholar
  6. 6.
    C. Baral and M. Gelfond. Logic programming and knowledge representation. Journal of Logic Programming 19/20:73–148, 1994.CrossRefMathSciNetGoogle Scholar
  7. 7.
    K. L. Clark. Negation as failure. In: H. Gallaire and J. Minker (eds.), Logic and Data Bases, Plenum Press, pp. 119–140, 1978.Google Scholar
  8. 8.
    M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In: Proc. 5th Int’l Conf. and Symp. on Logic Programming, MIT Press, pp. 1070–1080, 1988.Google Scholar
  9. 9.
    J. W. Lloyd. Foundations of logic programming (2nd edition), Springer-Verlag, 1987.Google Scholar
  10. 10.
    S. Muggleton. Duce, an oracle based approach to constructive induction. In: Proc. IJCAI-87, Morgan Kaufmann, pp. 287–292, 1987.Google Scholar
  11. 11.
    S. Muggleton. Inverting the resolution principle. In: Machine Intelligence, vol. 12, Oxford University Press, pp. 93–103, 1991.Google Scholar
  12. 12.
    S. Muggleton. Inductive Logic Programming. In [14], pp. 3–27, 1992.Google Scholar
  13. 13.
    S. Muggleton and W. Buntine. Machine invention of first-order predicate by inverting resolution. In: [14>], pp. 261–280.Google Scholar
  14. 14.
    S. Muggleton (ed.). Inductive Logic Programming, Academic Press, 1992.Google Scholar
  15. 15.
    T. C. Przymusinski. On the declarative semantics of deductive databases and logic programs. In: J. Minker (ed.), Foundations of Deductive Databases and Logic Programming, Morgan Kaufmann, pp. 193–216, 1988.Google Scholar
  16. 16.
    C. Rouveirol. Extension of inversion of resolution applied to theory completion. In: [14], pp. 63–92.Google Scholar
  17. 17.
    K. Taylor. Inverse resolution of normal clauses. In: Proc. ILP-93, J. Stefan Institute, pp. 165–177, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Chiaki Sakama
    • 1
  1. 1.Department of Computer and Communication SciencesWakayama University SakaedaniJapan

Personalised recommendations