Advertisement

Explicit representation of terms defined by counter examples

  • J. -L. Lassez
  • K. Marriott
Session 2 Logic Programming And Functional Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 241)

Abstract

Anti-unification guarantees the existence of a term which is an explicit representation of the most specific generalization of a collection of terms. This provides a formal basis for learning from examples. Here we address the dual problem of computing a generalization given a set of counter examples. Unlike learning from examples an explicit, finite representation for the generalization does not always exist. We show that the problem is decidable by providing an algorithm which, given an implicit representation will return a finite explicit representation or report that none exists. Applications of this result to the problem of negation as failure and to the representation of solutions to systems of equations and inequations are also mentioned.

Keywords

Function Symbol Explicit Representation Implicit Representation Specific Generalization Ground Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Cla78]
    K. Clark, Negation as Failure, Logic & Databases (Ed. H. Gallaire & J. Minker), Plenum Press, New York, 1978, 293–322.Google Scholar
  2. [Col84]
    A. Colmerauer, Equations and Inequations on Finite and Infinite Trees, FGCS'84 Proceedings, Nov. 1984.Google Scholar
  3. [Hue76]
    G. Huet, Resolution d'Equations Dans Des Langages D'Ordre 1,2, ..., ω (These d'Etat), Universite de Paris VII, Dec. 1976.Google Scholar
  4. [Hue80]
    G. Huet, Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems, JACM, Vol. 27, No. 4, Oct. 1980, 797–821.Google Scholar
  5. [JLL83]
    J. Jaffar, J-L. Lassez & J. Lloyd, Completeness of the Negation-As-Failure Rule, IJCAI-83, 1983, pp 500–506.Google Scholar
  6. [LaM86]
    J-L. Lassez & K. Marriott, Explicit Representation of Terms Defined by Counter Examples, Tech. Report, IBM Thomas J. Watson Lab.Google Scholar
  7. [LMM86]
    J-L. Lassez, M.J. Maher & K. Marriott, Unification Revisited, Tech. Report, IBM Thomas J. Watson Lab., Forthcoming.Google Scholar
  8. [Mic83]
    R.S. Michalski, A Theory and Methodology of Inductive Learning, Artificial Intelligence 20, 1983, 111–161.Google Scholar
  9. [Mit78]
    T.M. Mitchell, Version Spaces: An Approach to Concept Learning, (Ph.D Thesis), STAN-CS-78-711, Comp. Science Dept., Stanford University, Dec. 1978.Google Scholar
  10. [Nai85]
    L. Naish, The MU-Prolog 3.2 Reference Manual, Tech. Rpt. 85/11, Comp. Science Dept., Melbourne University, 1985.Google Scholar
  11. [Nai86]
    L. Naish, Negation & Quantifiers in NU-Prolog, Proc. 3rd Conf. on Logic Programming, July 1986.Google Scholar
  12. [Plo70]
    G.D. Plotkin, A Note on Inductive Generalization, Machine Intelligence 5, (B. Meltzer & D. Michie Eds.), 1970, 153–163.Google Scholar
  13. [Plo71]
    G.D. Plotkin, A Further Note on Inductive Generalization, Machine Intelligence 6, (B. Meltzer & D. Michie Eds.), 1971, 101–124.Google Scholar
  14. [Rey70]
    J.C. Reynolds, Transformational Systems and the Algebraic Structure of Atomic Formulas, Machine Intelligence 5, (B. Meltzer & D. Michie Eds.), 1970, 135–152.Google Scholar
  15. [Rob65]
    J.A. Robinson, A Machine-Oriented Logic Based on the Resolution Principle, JACM, Vol. 12, No. 1, Jan. 1965, pp 23–41.Google Scholar
  16. [Ver80]
    S.A. Vere, Multilevel Counterfactuals for Generalization of Relational Concepts and Productions, Artificial Intelligence 14, 1980, 139–164.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • J. -L. Lassez
    • 1
  • K. Marriott
    • 1
  1. 1.IBM Thomas J. Watson Research CenterYorktown Heights

Personalised recommendations