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The Generative Capacity of the Lambek–Grishin Calculus: A New Lower Bound

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Formal Grammar (FG 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5591))

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Abstract

The Lambek–Grishin calculus LG is a categorial type logic obtained by adding a family of connectives dual to the family { ⊗ , /, \}, and adding interaction postulates between the two families of connectives thus obtained. In this paper, we prove a new lower bound on the generative capacity of LG, namely the class of languages that are the intersection of a context-free language and the permutation closure of a context-free language. This implies that LG recognizes languages like the MIX language, e.g. the permutation closure of , and , which can not be recognized by tree adjoining grammars.

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Author information

Authors and Affiliations

  1. Universiteit Utrecht, The Netherlands

    Matthijs Melissen

  2. Université de Luxembourg, Luxembourg

    Matthijs Melissen

Authors
  1. Matthijs Melissen
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Editor information

Editors and Affiliations

  1. INRIA Nancy - Grand Est, 615 Rue du Jardin Botanique, 54600, Villers-lès-Nancy, France

    Philippe de Groote

  2. Institut für Anglistik und Amerikanistik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10117, Berlin, Germany

    Markus Egg

  3. Institut für Sprache und Information, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany

    Laura Kallmeyer

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Melissen, M. (2011). The Generative Capacity of the Lambek–Grishin Calculus: A New Lower Bound. In: de Groote, P., Egg, M., Kallmeyer, L. (eds) Formal Grammar. FG 2009. Lecture Notes in Computer Science(), vol 5591. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20169-1_8

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  • DOI: https://doi.org/10.1007/978-3-642-20169-1_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20168-4

  • Online ISBN: 978-3-642-20169-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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