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 ¿-sorted multimodal calculus mD. More concretely, we present a faithful embedding translation (·)# between mD and hD in such a way that it can be said that hD absorbs the structural rules of mD.

Capítol de llibre d'homenatge "Categories and Types in Logic, Language, and Physics. Essays Dedicated to Jim Lambek on the Occasion of His 90th Birthday"