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International Tbilisi Symposium on Logic, Language, and Computation

TbiLLC 2018: Language, Logic, and Computation pp 42–63Cite as

Finite Identification with Positive and with Complete Data

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11456))

  • The original version of this chapter was revised: One information in the acknowledgment was missing. This has now been rectified. The correction to this chapter is available at https://doi.org/10.1007/978-3-662-59565-7_18

Abstract

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.

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Change history

  • 27 August 2019

    By mistake the originally published version of this chapter did not include the acknowledgement text. This has been corrected so that the updated version of the chapter now contains the following acknowledgement: We want to thank Sebastiaan A. Terwijn for his assistance in the methods of the proof of Theorem 11. We thank the two anonymous referees that helped us to clarify a number of issues and improve the paper.

Notes

  1. 1.

    We write \(F_n\) for the finite set with canonical index n.

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Acknowledgment

We want to thank Sebastiaan A. Terwijn for his assistance in the methods of the proof of Theorem 11. We thank the two anonymous referees that helped us to clarify a number of issues and improve the paper.

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Authors and Affiliations

  1. Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands

    Dick de Jongh & Ana Lucia Vargas-Sandoval

Authors
  1. Dick de Jongh
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  2. Ana Lucia Vargas-Sandoval
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Corresponding author

Correspondence to Ana Lucia Vargas-Sandoval .

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Editors and Affiliations

  1. Department of Computer Science, University College London, London, UK

    Alexandra Silva

  2. Department of Computer Science, University of Oxford, Oxford, UK

    Sam Staton

  3. Department of Linguistics, Heinrich Heine University Düsseldorf, Düsseldorf, Germany

    Peter Sutton

  4. Leibniz-Zentrum Allgemeine Sprachwissenschaft, Berlin, Germany

    Carla Umbach

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de Jongh, D., Vargas-Sandoval, A.L. (2019). Finite Identification with Positive and with Complete Data. In: Silva, A., Staton, S., Sutton, P., Umbach, C. (eds) Language, Logic, and Computation. TbiLLC 2018. Lecture Notes in Computer Science(), vol 11456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-59565-7_3

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  • DOI: https://doi.org/10.1007/978-3-662-59565-7_3

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  • Print ISBN: 978-3-662-59564-0

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