Skip to main content

Constructing refinement operators by decomposing logical implication

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 728))

Abstract

Inductive learning models [15] [18] often use a search space of clauses, ordered by a generalization hierarchy. To find solutions in the model, search algorithms use different generalization and specialization operators. In this article we introduce a framework for deconstructing orderings into operators. We will decompose the quasi-ordering induced by logical implication into six increasingly weak orderings. The difference between two successive orderings will be small, and can therefore be understood easily. Using this decomposition, we will describe upward and downward refinement operators for all orderings, including θ-subsumption and logical implication.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Bain and S.H. Muggleton. Non-monotonic Learning. Machine Intelligence, 12, 1991.

    Google Scholar 

  2. W. Buntine. Generalised Subsumption and its Applications to Induction and Redundancy. Artificial Intelligence, 36(2):149–176, 1988.

    Google Scholar 

  3. N. Helft. Inductive Generalization: A Logical Framework. In I. Bratko and N. Lavrac, editor, EWSL-87, pages 149–157. Sigma Press, Wilmslow, England, 1987.

    Google Scholar 

  4. P.D. Laird. Learning from Good and Bad Data. Kluwer Academic Publishers, 1988.

    Google Scholar 

  5. S. Lapointe and S. Matwin. Subunification: A Tool for Efficient Induction of Recursive Programs. In ML-92, pages 273–280, Aberdeen, 1992. Morgan Kaufmann.

    Google Scholar 

  6. C. Lee. A completeness theorem and a computer program for finding theorems derivable from given axioms. PhD thesis, University of California, Berkely, 1967.

    Google Scholar 

  7. C. Ling and M. Dawes. SIM the Inverse of Shapiro's MIS. Technical report, Department of Computer Science, University of Western Ontario, London, Ontario, Canada., 1990.

    Google Scholar 

  8. T.M. Mitchell. Generalization as Search. Artificial Intelligence, 18:203–226, 1982.

    Google Scholar 

  9. S.H. Muggleton. Inductive logic programming. In First Conference on Algorithmic Learning Theory, Ohmsha, Tokyo, 1990. Invited paper.

    Google Scholar 

  10. S.H. Muggleton. Inverting Logical Implication. preprint, 1992.

    Google Scholar 

  11. S.H. Muggleton and C. Feng. Efficient Induction of Logic Programs. In First Conference on Algorithmic Learning Theory, Ohmsha, Tokyo, 1990.

    Google Scholar 

  12. T. Niblett. A Study of Generalisation in Logic Programs. In EWSL-88, pages 131–138. Pitman, 1988.

    Google Scholar 

  13. S.H. Nienhuys-Cheng. Generalization and Refinement. Technical report, Erasmus University Rotterdam, Dept. of Computer Science, August 1992. Preprint.

    Google Scholar 

  14. G.D. Plotkin. A Note on Inductive Generalization. Machine Intelligence, 5:153–163, 1970.

    Google Scholar 

  15. G.D. Plotkin. A Further Note on Inductive Generalization. Machine Intelligence, 6:101–124, 1971.

    Google Scholar 

  16. G.D. Plotkin. Automatic Methods of Inductive Inference. PhD thesis, Edinburgh University, Edinburgh, August 1971.

    Google Scholar 

  17. J.C. Reynolds. Transformational Systems and the Algebraic Structure of Atomic Formulas. Machine Intelligence, 5:135–153, 1970.

    Google Scholar 

  18. E.Y. Shapiro. Inductive Inference of Theories from Facts. Technical Report 192, Department of Computer Science, Yale University, New Haven. CT., 1981.

    Google Scholar 

  19. P.R.J. Van der Laag and S.H. Nienhuys-Cheng. A Locally Finite and Complete Upward Refinement Operator for θ-Subsumption. In Benelearn-93, Artificial Intelligence Laboratory, Vrije Universiteit Brussel, 1993.

    Google Scholar 

  20. P.R.J. Van der Laag and S.H. Nienhuys-Cheng. Subsumption and Refinement in Model Inference. In ECML-93, pages 95–114, 1993.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Pietro Torasso

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nienhuys-Cheng, SH., van der Laag, P.R.J., van der Torre, L.W.N. (1993). Constructing refinement operators by decomposing logical implication. In: Torasso, P. (eds) Advances in Artificial Intelligence. AI*IA 1993. Lecture Notes in Computer Science, vol 728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57292-9_56

Download citation

  • DOI: https://doi.org/10.1007/3-540-57292-9_56

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57292-3

  • Online ISBN: 978-3-540-48038-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics