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Undecidability of a Newly Proposed Calculus for CatLog3

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Formal Grammar (FG 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11668))

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Abstract

In his recent papers “Parsing/theorem-proving for logical grammar CatLog3” and “A note on movement in logical grammar”, Glyn Morrill proposes a new substructural calculus to be used as the basis for the categorial grammar parser CatLog3. In this paper we prove that the derivability problem for a fragment of this calculus is algorithmically undecidable.

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Acknowledgments

The authors are thankful to the anonymous referees for helpful comments and interesting questions. They would also like to thank Glyn Morrill for fruitful discussions of linguistic motivations for the calculi Morrill introduced in [27,28,29, 31, 32], which are considered in this paper.

Funding

The work of Max Kanovich and Andre Scedrov was supported by the Russian Science Foundation under grant 17-11-01294 and performed at National Research University Higher School of Economics, Moscow, Russia. The work of Stepan Kuznetsov was supported by the Young Russian Mathematics award, by the grant MK-430.2019.1 of the President of Russia, and by the Russian Foundation for Basic Research grant 18-01-00822. Section 3 was contributed by Kanovich and Scedrov. Section 4 was contributed by Kuznetsov. Sections 1, 2, and 5 were contributed jointly and equally by all co-authors.

Author information

Authors and Affiliations

  1. University College London, London, UK

    Max Kanovich

  2. Steklov Mathematical Institute of the RAS, Moscow, Russia

    Stepan Kuznetsov

  3. University of Pennsylvania, Philadelphia, USA

    Andre Scedrov

  4. National Research University Higher School of Economics, Moscow, Russia

    Max Kanovich, Stepan Kuznetsov & Andre Scedrov

  5. Institute of Oriental Studies of the RAS, Languages Department, Moscow, Russia

    Max Kanovich

Authors
  1. Max Kanovich
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  2. Stepan Kuznetsov
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  3. Andre Scedrov
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Corresponding author

Correspondence to Stepan Kuznetsov .

Editor information

Editors and Affiliations

  1. University of Trento, Povo, Italy

    Raffaella Bernardi

  2. Universität Leipzig, Leipzig, Germany

    Greg Kobele

  3. LORIA, Inria Nancy, Villers-lès-Nancy, France

    Sylvain Pogodalla

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Kanovich, M., Kuznetsov, S., Scedrov, A. (2019). Undecidability of a Newly Proposed Calculus for CatLog3. In: Bernardi, R., Kobele, G., Pogodalla, S. (eds) Formal Grammar. FG 2019. Lecture Notes in Computer Science(), vol 11668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-59648-7_5

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  • DOI: https://doi.org/10.1007/978-3-662-59648-7_5

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