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International Conference on Logical Aspects of Computational Linguistics

LACL 2001: Logical Aspects of Computational Linguistics pp 158–174Cite as

On Mixing Deduction and Substitution in Lambek Categorial Grammars

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2099))

Abstract

Recently, learning algorithms in Gold’s model [Gol67] have been proposed for some particular classes of classical categorial grammars [Kan98]. We are interested here in learning Lambek categorial grammars.

In general grammatical inference uses unification and substitution. In the context of Lambek categorial grammars it seems appropriate to incorporate an operation on types based both on deduction (Lambek derivation) and on substitution instead of standard substitution and standard unification.

The purpose of this paper is to investigate such operations defined both in terms of deduction and substitution in categorial grammars and to study a modified unification that may serve as a basis for learning in this framework. We consider some variants of definition : in particular we show that deduction and substitution do not permute. We then consider a modified unification, here called ∥= -unification :we give a criterion for the existence and construction of ∥= -unifiers in terms of group issues.

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Author information

Authors and Affiliations

  1. Campus de Beaulieu, IRISA and University of Rennes1, 35042, Rennes Cedex, France

    Annie Foret

Authors
  1. Annie Foret
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Editor information

Editors and Affiliations

  1. INRIA Lorraine, 615 rue du Jardin Botanique, B.P. 101, 54602, Villers-lès-Nancy Cedex, France

    Philippe de Groote

  2. Universitat Politècnica de Catalunya, Jordi Girona Salgado, 1-3, 08028, Barcelona, Spain

    Glyn Morrill

  3. Faculté des Sciences, Institut de recherche en Informatique de Nantes (IRIN), 2, rue de la Houssinière, B.P. 92208, 44322, Nantes Cedex 03, France

    Christian Retoré

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© 2001 Springer-Verlag Berlin Heidelberg

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Foret, A. (2001). On Mixing Deduction and Substitution in Lambek Categorial Grammars. In: de Groote, P., Morrill, G., Retoré, C. (eds) Logical Aspects of Computational Linguistics. LACL 2001. Lecture Notes in Computer Science(), vol 2099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48199-0_10

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  • DOI: https://doi.org/10.1007/3-540-48199-0_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42273-0

  • Online ISBN: 978-3-540-48199-7

  • eBook Packages: Springer Book Archive

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