Learning Lambek Grammars from Proof Frames

  title={Learning Lambek Grammars from Proof Frames},
  author={Roberto Bonato and Christian Retor{\'e}},
  booktitle={Categories and Types in Logic, Language, and Physics},
  • R. Bonato, C. Retoré
  • Published in
    Categories and Types in Logic…
    1 October 2013
  • Computer Science
In addition to their limpid interface with semantics, categorial grammars enjoy another important property: learnability. This was first noticed by Buskowsky and Penn and further studied by Kanazawa, for Bar-Hillel categorial grammars. What about Lambek categorial grammars? In a previous paper we showed that product free Lambek grammars where learnable from structured sentences, the structures being incomplete natural deductions. These grammars were shown to be unlearnable from strings by… 
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A Study on Learnability for Rigid Lambek Grammars
  • R. Bonato
  • Computer Science, Linguistics
  • 2006
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  • M. Pentus
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  • 1993
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