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

  • Matthijs Melissen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5591)

Abstract

The Lambek–Grishin calculus LG is a categorial type logic obtained by adding a family of connectives Open image in new window 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 Open image in new window , and Open image in new window , which can not be recognized by tree adjoining grammars.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Matthijs Melissen
    • 1
    • 2
  1. 1.Universiteit UtrechtThe Netherlands
  2. 2.Université de LuxembourgLuxembourg

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