Using constraints to building version spaces

  • Michèle Sebag
Regular Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 784)


Our concern is building the set G of maximally general terms covering positive examples and rejecting negative examples in prepositional logic.

Negative examples are represented as constraints on the search space. This representation allows for defining a partial order on the negative examples and on attributes too. It is shown that only minimal negative examples and minimal attributes are to be considered when building the set G. These results hold in case of a non-convergent data set.

Constraints can be directly used for a polynomial characterization of G. They also allow for detecting erroneous examples in a data set.


  1. 1.
    F. Bergadano, A Giordana, A Knowledge Intensive Approach to Concept Induction, ICML 1988, pp 305–317.Google Scholar
  2. 2.
    A. Bundy, B. Silver, D. Plummer, An analytical Comparizon of Some Rule Learning Programs, Artificial Intelligence, 27, 1985, pp 137–181.CrossRefGoogle Scholar
  3. 3.
    P. Clark T. Niblett Induction in noisy domains Progress in machine learning, Proc. EWSL 1987, I. Bratko N. Lavrac Eds, Sigma Press.Google Scholar
  4. 4.
    D. Haussler, Quantifying Inductive Bias: AI Learnign Algorithms and Valiant's Learning Framework, Artificial Intelligence, 36, 1988, pp 177–221.CrossRefGoogle Scholar
  5. 5.
    H. Hirsh, Polynomial-Time Learning with Version Spaces, Proc. National Conference on Artificial Intelligence, 1992 pp 117–122.Google Scholar
  6. 6.
    Michalski R.S. A theory and methodology for inductive learning Machine Learning: An Artificial Intelligence Approach, I, R.S. Michalski, J.G. Carbonnell, T.M. Mitchell Eds, Springer Verlag, (1983), p 83–134.Google Scholar
  7. 7.
    T.M. Mitchell, Generalization as Search, Artificial Intelligence Vol 18, pp 203–226, 1982.CrossRefGoogle Scholar
  8. 8.
    J. Nicolas, Une Représentation Efficace pour les Espaces de Version, JFA 1993.Google Scholar
  9. 9.
    J. Piaget, Six études de psychologie, Denoel 1964.Google Scholar
  10. 10.
    R. Quinlan, The effect of noise on concept learning Machine Learning: An Artificial Intelligence Approach, I, R.S. Michalski, J.G. Carbonnell, T.M. Mitchell Eds, Vol 2, Morgan Kaufman, 1986.Google Scholar
  11. 11.
    B. Smith, P. Rosenbloom, Incremental non-backtracking focussing: A polynomially-bounded generalization algorithm for version space, Proc. National Conference on Artificial Intelligence, 1990, pp 848–853.Google Scholar
  12. 12.
    P.H. Winston, Learning Structural Descriptions from Examples The Psychology of Computer Vision, P.H. Winston Ed, Mc Graw Hill, New York, 1975, pp 157–209.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Michèle Sebag
    • 1
  1. 1.LMS-CNRS URA 317Ecole PolytechniquePalaiseau CedexFrance

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