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A Class of Prolog Programs with Non-linear Outputs Inferable from Positive Data

  • M. R. K. Krishna Rao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3734)

Abstract

In this paper, we study inferability of Prolog programs from positive examples alone. We define a class of Prolog programs called recursion bounded programs that can capture non-linear relationships between inputs and outputs and yet inferable from positive examples. This class is rich enough to include many programs like append, delete, insert, reverse, permute, count, listsum, listproduct, insertion-sort, quick-sort on lists, various tree traversal programs and addition, multiplication, factorial, power on natural numbers. The relation between our results and the known results is also discussed. In particular, the class of recursion bounded programs contains all the known terminating linearly-moded Prolog programs of Krishna Rao [7] and additional programs like power on natural numbers which do not belong to the class of linearly-moded programs and the class of safe programs of Martin and Sharma [12].

Keywords

Logic Program Inductive Inference Positive Data Semantic Mapping Safe Program 
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.

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References

  1. 1.
    Angluin, D.: Inductive inference of formal languages from positive data. Information and Control 45, 117–135 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Apt, K.R., Pedreschi, D.: Reasoning about termination of pure Prolog programs. Information and Computation 106, 109–157 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Arimura, H., Shinohara, T., Otsuki, S.: In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds.) STACS 1994. LNCS, vol. 775, pp. 649–660. Springer, Heidelberg (1994)Google Scholar
  4. 4.
    Arimura, H., Shinohara, T.: Inductive inference of Prolog programs with linear data dependency from positive data. In: Proc. Information Modelling and Knowledge Bases V, pp. 365–375. IOS press, Amsterdam (1994)Google Scholar
  5. 5.
    Blum, L., Blum, M.: Towards a mathematical theory of inductive inference. Information and Control 28, 125–155 (1975)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gold, E.M.: Language identification in the limit. Information and Control 10, 447–474 (1967)zbMATHCrossRefGoogle Scholar
  7. 7.
    Krishna Rao, M.R.K.: Some classes of Prolog programs inferable from positive data. Theor. Comput. Sci. 241, 211–234 (2000)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Krishna Rao, M.R.K.: Inductive inference of term rewriting systems from positive data. In: Ben-David, S., Case, J., Maruoka, A. (eds.) ALT 2004. LNCS (LNAI), vol. 3244, pp. 69–82. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Krishna Rao, M.R.K., Shyamasundar, R.K.: Unification-free execution of well-moded Prolog programs. In: Mycroft, A. (ed.) SAS 1995. LNCS, vol. 983, pp. 243–260. Springer, Heidelberg (1995)Google Scholar
  10. 10.
    Lloyd, J.W.: Foundations of Logic Programming. Springer, Heidelberg (1987)zbMATHGoogle Scholar
  11. 11.
    Martin, E.: Personal communication (2005)Google Scholar
  12. 12.
    Martin, É., Sharma, A.: On sufficient conditions for learnability of logic programs from positive data. In: Džeroski, S., Flach, P.A. (eds.) ILP 1999. LNCS (LNAI), vol. 1634, pp. 198–209. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  13. 13.
    Shapiro, E.: Inductive inference of theories from facts, Tech. Rep., Yale Univ. (1981)Google Scholar
  14. 14.
    Shapiro, E.: Algorithmic Program Debugging. MIT Press, Cambridge (1983)Google Scholar
  15. 15.
    Shinohara, T.: Inductive inference of monotonic formal systems from positive data. New Generation Computing 8, 371–384 (1991)zbMATHCrossRefGoogle Scholar
  16. 16.
    Shinohara, T., Arimura, H.: Inductive inference of unbounded unions of pattern languages from positive data. Theor. Comput. Sci. 241, 191–209 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Sterling, L., Shapiro, E.: The Art of Prolog. MIT Press, Cambridge (1994)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • M. R. K. Krishna Rao
    • 1
  1. 1.Information and Computer Science DepartmentKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia

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