The Hidden Structural Rules of the Discontinuous Lambek Calculus

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


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.


Structural Term Atomic Type Structural Rule Sequent Calculus Constructive Proof 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Universitat Politècnica de CatalunyaSpain

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