Polarized Montagovian Semantics for the Lambek-Grishin Calculus

  • Arno Bastenhof
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7395)

Abstract

Grishin ([9]) proposed enriching the Lambek calculus with multiplicative disjunction (par) and coresiduals. Applications to linguistics were discussed by Moortgat ([14]), who spoke of the Lambek-Grishin calculus (LG). In this paper, we adapt Girard’s polarity-sensitive double negation embedding for classical logic ([7]) to extract a compositional Montagovian semantics from a display calculus for focused proof search ([1]) in LG. We seize the opportunity to illustrate our approach alongside an analysis of extraction, providing linguistic motivation for linear distributivity of tensor over par ([3]), thus answering a question of [10]. We conclude by comparing our proposal to that of [2], where alternative semantic interpretations of LG are considered on the basis of call-by-name and call-by-value evaluation strategies.

Keywords

Noun Phrase Natural Deduction Sequent Calculus Lexical Semantic Positive Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Arno Bastenhof
    • 1
  1. 1.Utrecht UniversityThe Netherlands

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