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Generalization under implication by using or-introduction

  • Peter Idestam-Almquist
Research Papers Inductive Logic Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 667)

Abstract

In the area of inductive learning, generalization is a main operation. Already in the early 1970's Plotkin described algorithms for computation of least general generalizations of clauses under θ-subsumption. However, there is a type of generalizations, called roots of clauses, that is not possible to find by generalization under θ-subsumption. This incompleteness is important, since almost all inductive learners that use clausal representation perform generalization under θ-subsumption.

In this paper a technique to eliminate this incompleteness, by reducing generalization under implication to generalization under θ-subsumption, is presented. The technique is conceptually simple and is based on an inference rule from natural deduction, called or-introduction. The technique is proved to be sound and complete, but unfortunately it suffers from complexity problems.

References

  1. 1.
    M. Bain and S. Muggleton. Non-monotonic learning. Machine Intelligence, 12, 1991.Google Scholar
  2. 2.
    Jean H. Gallier. Logic for Computer Science: Foundations of Automatic Theorem Proving. John Wiley & Sons, 1987.Google Scholar
  3. 3.
    P. Idestam-Almquist. Generalization under implication by recursive antiunification. Submitted to the International Workshop on Inductive Logic Programming 1993.Google Scholar
  4. 4.
    P. Idestam-Almquist. Generalization under implication. Technical report, Department of Computer and Systems Sciences, Stockholm University, 1992. Report 92-020-SYSLAB.Google Scholar
  5. 5.
    P. Idestam-Almquist. Learning missing clauses by inverse resolution. In Proceedings of the International Conference on Fifth Generation Computer Systems 1992, Ohmsha, Tokyo, 1992.Google Scholar
  6. 6.
    Stéphane Lapointe and Stan Matwin. Sub-unification: A tool for efficient induction of recursive programs. In Proceedings of the Ninth International Conference on Machine Learning. Morgan Kaufmann, 1992.Google Scholar
  7. 7.
    J. W. Lloyd. Foundations of Logic Programming. Springer-Verlag, 1987. Second edition.Google Scholar
  8. 8.
    Stephen Muggleton. Inductive logic programming. New Generation Computing, 8(4):295–318, 1991.Google Scholar
  9. 9.
    Stephen Muggleton. Inverting implication. In Stephen Muggleton, editor, Proceedings of the International Workshop on Inductive Logic Programming, 1992.Google Scholar
  10. 10.
    Stephen Muggleton and Wray Buntine. Machine invention of first-order predicates by inverting resolution. In Proceedings of the Fifth International Conference on Machine Learning. Morgan Kaufmann, 1988.Google Scholar
  11. 11.
    Stephen Muggleton and C. Feng. Efficient induction of logic programs. In Proceedings of the First Conference on Algorithmic Learning Theory, Tokyo, 1990. Ohmsha Publishers.Google Scholar
  12. 12.
    Tim Niblett. A study of generalization in logic programs. In Proceedings of the Third European Working Session on Learning. Pitman, 1988.Google Scholar
  13. 13.
    Nilsson and Genesereth. Logic Foundations of Artificial Intelligence. Morgan Kaufmann, 1987.Google Scholar
  14. 14.
    G. D. Plotkin. Automatic Methods of Inductive Inference. PhD thesis, Edinburgh University, 1971.Google Scholar
  15. 15.
    J. Robinson. A machine-oriented logic based on the resolution principle. Journal of the ACM, 12(1), 1965.Google Scholar
  16. 16.
    Céline Rouveirol. Extensions of inversion of resolution applied to theory completion. In Stephen Muggleton, editor, Inductive Logic Programming. Academic Press, San Diego, CA, 1992.Google Scholar
  17. 17.
    Céline Rouveriol and Jean François Puget. Beyond inversion of resolution. In Proceedings of the Seventh International Conference on Machine Learning. Morgan Kaufmann, 1990.Google Scholar
  18. 18.
    Richmond H. Thomason. Symbolic Logic—An Introduction. McMillan Publishers, 1970.Google Scholar
  19. 19.
    Ruediger Wirth. Completing logic programs by inverse resolution. In Proceedings of the Fourth Working Session on Learning. Pitman, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Peter Idestam-Almquist
    • 1
  1. 1.Department of Computer and Systems SciencesStockholm UniversityKistaSweden

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