Polarized Montagovian Semantics for the Lambek-Grishin Calculus

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


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.


Noun Phrase Natural Deduction Sequent Calculus Lexical Semantic Positive Formula 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

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