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)


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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© 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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