Learning from Positive Data Based on the MINL Strategy with Refinement Operators

  • Seishi Ouchi
  • Akihiro Yamamoto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6284)


In the present paper we clarify the combination of the MINL (MINimal Langugae) strategy and refinement operators in the model of identification in the limit from positive data, by giving a learning procedure in a general form adopting both of the two. The MINL strategy is to choose minimal concepts consistent with given examples as guesses, and has been adopted in many previous works in the model. The minimality of concepts is defined w.r.t. the set-inclusion relation, and so the strategy is semantic-based. Refinement operators have developed in the field of learning logic programs to construct logic programs as hypotheses consistent with logical formulae given as examples. The operators are defined based on inference rules in first-order logic and so are syntactical. With the proposed procedure we give such a new class of tree pattern languages that every finite unions of the languages is identifiable from positive data without assuming the upperbound of the number of unions. Moreover, we revise the algorithm so that we can show that the class is polynomial time identifiable.


Polynomial Time Tree Pattern Function Symbol Concept Class Principal Symbol 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Angluin, D.: Inductive inference of formal languages from positive data. Information and Control 45, 117–135 (1980)CrossRefzbMATHGoogle Scholar
  2. 2.
    Angluin, D.: Inference of reversible languages. Journal of the ACM 29, 741–765 (1982)CrossRefzbMATHGoogle Scholar
  3. 3.
    Arimura, H., Ishizaka, H., Shinohara, T.: Learning unions of tree patterns using queries. In: Zeugmann, T., Shinohara, T., Jantke, K.P. (eds.) ALT 1995. LNCS, vol. 997, pp. 66–79. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  4. 4.
    Arimura, H., Shinohara, T., Otsuki, S.: A polynomial time algorithm for finding finite unions of tree pattern languages. In: Brewka, G., Jantke, K.P., Schmitt, P.H. (eds.) NIL 1991. LNCS (LNAI), vol. 659, pp. 118–131. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  5. 5.
    Gold, E.M.: Language identification in the limit. Information and Control 10, 447–474 (1967)CrossRefzbMATHGoogle Scholar
  6. 6.
    Goldman, S.A., Kwek, S.: On learning unions of pattern languages and tree patterns in the mistake bound model. Theoretical Computer Science 288, 237–254 (2000)CrossRefzbMATHGoogle Scholar
  7. 7.
    Kobayashi, S.: Approximate identification, finite elasticity and lattice structure of hypothesis space. In: Technical Report, CSIM 96-04, Department of Computer Science and Information Mathematics. University of Electro-Communications (1996)Google Scholar
  8. 8.
    Laird, P.D.: Learning from Good and Bad Data. Kluwer Academic Publishers, Dordrecht (1988)CrossRefzbMATHGoogle Scholar
  9. 9.
    Lange, S., Zilles, S.: On the learnability of erasing pattern languages in the query model. In: Gavaldá, R., Jantke, K.P., Takimoto, E. (eds.) ALT 2003. LNCS (LNAI), vol. 2842, pp. 129–143. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Lassez, J.L., Maher, M.J., Marriott, K.: Unification revisited. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 587–625. Morgan Kaufmann, San Francisco (1988)CrossRefGoogle Scholar
  11. 11.
    Motoki, T., Shinohara, T., Wright, K.: The correct definition of finite elasticity. In: Proceedings of the fourth annual workshop on Computational learning theory (COLT 1991), p. 375 (1991)Google Scholar
  12. 12.
    Plotkin, G.D.: A note on inductive generalization. Machine Intelligence 5, 153–163 (1970)zbMATHGoogle Scholar
  13. 13.
    Sakakibara, Y., Kobayashi, S., Yokomori, T.: Computational Learning Theory, Baifukan (2001) (in Japanese)Google Scholar
  14. 14.
    Shapiro, E.Y.: Inductive inference of theories from facts. In: Research Report YALEU/DCS/RR-192. Department of Computer Science, Yale University (1980)Google Scholar
  15. 15.
    Shinohara, T., Arikawa, S.: Pattern inference. In: Lange, S., Jantke, K.P. (eds.) GOSLER 1994. LNCS, vol. 961, pp. 259–291. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  16. 16.
    Shinohara, T., Arimura, H.: Inductive inference of unbounded unions of pattern languages from positive data. Theoretical Computer Science 241, 191–209 (2000)CrossRefzbMATHGoogle Scholar
  17. 17.
    Wright, K.: Identification of unions of languages drawn from an identifiable class. In: Proceedings of the Second Annual Workshop on Computational Learning Theory (COLT 1989), pp. 328–333 (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Seishi Ouchi
    • 1
  • Akihiro Yamamoto
    • 1
  1. 1.Graduate School of InformaticsKyoto UniversityKyotoJapan

Personalised recommendations