Studia Logica

, Volume 85, Issue 2, pp 153–169 | Cite as

On Learnability of Restricted Classes of Categorial Grammars



In this paper we present learning algorithms for classes of categorial grammars restricted by negative constraints. We modify learning functions of Kanazawa [10] and apply them to these classes of grammars. We also prove the learnability of intersection of the class of minimal grammars with the class of k-valued grammars.


categorial grammar unification learning function learning algorithm 


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  1. 1.
    Ajdukiewicz K. (1935) ‘Die syntaktische Konnexität’. Studia Philosophica 1:1–27Google Scholar
  2. 2.
    Bar-Hillel, Y., C. Gaifman, and E. Shamir, ‘On categorial and phrase structure grammars’, Bull. Res. Counc.:155–166, Israel, 1960.Google Scholar
  3. 3.
    Béchet, D., and A. Foret, ‘K-valued non-associative Lambek categorial grammars are not learnable from strings’, in ACL (eds.), Proccedings of the 41st Annual Meeting of the Association for Computational Linguistics (ACL 2003), 2003, pp. 351–358.Google Scholar
  4. 4.
    Buszkowski W. (1987) ‘Solvable problems for classical categorial grammars’. Bulletin of the Polish Academy of Sciences, Mathematics 35:373–382Google Scholar
  5. 5.
    Buszkowski, W., and B. Dziemidowicz, ‘Restricted optimal unification’, in Y. Hamamatsu,W. Kosicki,L. Polkowski,M. Toho, and T. Yonekura (eds.), Formal Methods and Intelligent Techniques in Control, Decision Making, Multimedia and Robotics, Warszawa, 2000, pp. 1–8.Google Scholar
  6. 6.
    Buszkowski W., Penn G. (1990) ‘Categorial grammars determined from linguistic data by unification’. Studia Logica 49:431–454CrossRefGoogle Scholar
  7. 7.
    Dziemidowicz B. (2002). ‘Optimal unification and learning algorithms for categorial grammars’. Fundamenta Informaticae 49:297–308Google Scholar
  8. 8.
    Gold E.M. (1967) ‘Language identification in the limit’. Information and Control 10:447– 474CrossRefGoogle Scholar
  9. 9.
    Kanazawa M. (1996). ‘Identification in the limit of categorial grammars’. Journal of Logic, Language and Information 5:115–155CrossRefGoogle Scholar
  10. 10.
    Kanazawa M. (1998) ‘Learnable classes of categorial grammars’. CSLI Publications FoLLI, StanfordGoogle Scholar
  11. 11.
    Kapur, S., ‘Computational learning of languages’, Ph. D. Thesis, Cornel University, report, 1991, pp. 91–1234.Google Scholar
  12. 12.
    Lloyd J.W. (1987) ‘Foundations of logic programming’. Springer, BerlinGoogle Scholar
  13. 13.
    Marciniec J. (1994) ‘Learning categorial grammars by unification with negative constraints’. Journal of Applied Non-Classical Logics 4:181–200Google Scholar
  14. 14.
    Marciniec J. (1997). ‘The method of unification in procedures of determining categorial grammars’ (in Polish). Investigationes Linguisticae 2:45–96Google Scholar
  15. 15.
    Osheron D., de Jongh D., Martin E., Weinstein S. ‘Formal learning theory’, in J. van Benthen and A. ter Meulen (eds.), Handbook of Logic and Language, 1997, pp. 737–775.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceUniversity of Warmia and MazuryOlsztynPoland

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