Finite Identification with Positive and with Complete Data

  • Dick de Jongh
  • Ana Lucia Vargas-SandovalEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11456)


We study the differences between finite identifiability of recursive languages with positive and with complete data. In finite families the difference lies exactly in the fact that for positive identification the families need to be anti-chains, while in the infinite case it is less simple, being an anti-chain is no longer a sufficient condition. We also study maximal learnable families, identifiable families with no proper extension which can be identified. We show that these often though not always exist with positive identification, but that with complete data there are no maximal learnable families at all. We also investigate a conjecture of ours, namely that each positively identifiable family has either finitely many or uncountably many maximal noneffectively positively identifiable extensions. We verify this conjecture for the restricted case of families of equinumerous finite languages.


Formal learning theory Finite identification Positive data Complete data Indexed family Anti-chains 



We thank the two anonymous referees that helped us to clarify a number of issues and improve the paper.


  1. 1.
    Angluin, D.: Inductive inference of formal languages from positive data. Inf. Control 45(2), 117–135 (1980)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bolander, T., Gierasimczuk, N.: Learning actions models: qualitative approach. In: van der Hoek, W., Holliday, W.H., Wang, W. (eds.) LORI 2015. LNCS, vol. 9394, pp. 40–52. Springer, Heidelberg (2015). Scholar
  3. 3.
    Bolander, T., Gierasimczuk, N.: Learning to act: qualitative learning of deterministic action models. J. Log. Comput. 28(2), 337–365 (2017)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Dégremont, C., Gierasimczuk, N.: Finite identification from the viewpoint of epistemic update. Inf. Comput. 209(3), 383–396 (2011)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Gierasimczuk, N., de Jongh, D.: On the complexity of conclusive update. Comput. J. 56(3), 365–377 (2012)CrossRefGoogle Scholar
  6. 6.
    Gierasimczuk, N., Hendricks, V.F., de Jongh, D.: Logic and learning. In: Baltag, A., Smets, S. (eds.) Johan van Benthem on Logic and Information Dynamics, pp. 267–288. Springer, Cham (2014). Scholar
  7. 7.
    Gold, M.E.: Language identification in the limit. Inf. Control 10(5), 447–474 (1967)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hiller, S., Fernández, R.: A data-driven investigation of corrective feedback on subject omission errors in first language acquisition. In: Proceedings of the 20th SIGNLL, Conference on Computational Natural Language Learning (CoNLL), pp. 105–114 (2016)Google Scholar
  9. 9.
    Jain, S., Osherson, D., Royer, J.S., Sharma, A.: Systems That Learn, vol. 2. MIT Press, Cambridge (1999)Google Scholar
  10. 10.
    Lange, S., Zeugmann, T.: Set-driven and rearrangement-independent learning of recursive languages. Theory Comput. Syst. 29(6), 599–634 (1996)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Mitkov, R.: The Oxford Handbook of Computational Linguistics. Oxford University Press, Oxford (2005)zbMATHGoogle Scholar
  12. 12.
    Mukouchi, Y.: Characterization of finite identification. In: Jantke, K.P. (ed.) AII 1992. LNCS, vol. 642, pp. 260–267. Springer, Heidelberg (1992). Scholar
  13. 13.
    Osherson, D.N., Stob, M., Weinstein, S.: Systems That Learn: An Introduction to Learning Theory for Cognitive and Computer Scientists. MIT Press, Cambridge (1986)Google Scholar
  14. 14.
    Rogers, H.: Theory of Recursive Functions and Effective Computability, vol. 5. McGraw-Hill, New York (1967)zbMATHGoogle Scholar
  15. 15.
    Saxton, M., Backley, P., Gallaway, C.: Negative input for grammatical errors: effects after a lag of 12 weeks. J. Child Lang. 32(3), 643–672 (2005)CrossRefGoogle Scholar
  16. 16.
    Soare, R.I.: Recursively Enumerable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets. Springer, Heidelberg (1999)zbMATHGoogle Scholar

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands

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