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The Hidden Structural Rules of the Discontinuous Lambek Calculus

Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8222)

Abstract

The sequent calculus sL for the Lambek calculus L ([2]) has no structural rules. Interestingly, sL is equivalent to a multimodal calculus mL, which consists of the nonassociative Lambek calculus with the structural rule of associativity. This paper proves that the sequent calculus or hypersequent calculus hD of the discontinuous Lambek calculus ([7], [4] and [8]), which like sL has no structural rules, is also equivalent to an ω-sorted multimodal calculus mD. More concretely, we present a faithful embedding translation \((\cdot)^\sharp\) between mD and hD in such a way that it can be said that hD absorbs the structural rules of mD.

Keywords

Structural Term Atomic Type Structural Rule Sequent Calculus Constructive Proof 
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 2014

Authors and Affiliations

  1. 1.Universitat Politècnica de CatalunyaSpain

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