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Minimalist Grammars in the Light of Logic

Sylvain Salvati 1, 2, * 
* Corresponding author
1 SIGNES - Linguistic signs, grammar and meaning: computational logic for natural language
Université Sciences et Technologies - Bordeaux 1, Inria Bordeaux - Sud-Ouest, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : In this paper, we aim at understanding the derivations of minimalist grammars without the shortest move constraint. This leads us to study the relationship of those derivations with logic. In particular we show that the membership problem of minimalist grammars without the shortest move constraint is as difficult as provability in Multiplicative Exponential Linear Logic. As a byproduct, this result gives us a new representation of those derivations with linear $\lambda$-terms. We show how to interpret those terms in a homomorphic way so as to recover the sentence they analyse. As the homorphisms we describe are rather evolved, we turn to a proof-net representation and explain how Monadic Second Order Logic and related techniques allow us both to define those proof-nets and to retrieve the sentence they analyse.
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Submitted on : Tuesday, February 8, 2011 - 5:16:41 PM
Last modification on : Saturday, June 25, 2022 - 8:29:55 PM
Long-term archiving on: : Tuesday, November 6, 2012 - 1:35:23 PM

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Sylvain Salvati. Minimalist Grammars in the Light of Logic. [Research Report] 2011, pp.39. ⟨inria-00563807⟩

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