Article

Journal of Logic, Language and Information

, Volume 11, Issue 2, pp 227-249

First online:

Substructural Logics with Mingle

  • Norihiro KamideAffiliated withWakayama National College of Technology

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Abstract

We introduce structural rules mingle, and investigatetheorem-equivalence, cut- eliminability, decidability, interpolabilityand variable sharing property for sequent calculi having the mingle.These results include new cut-elimination results for the extendedlogics: FLm (full Lambek logic with the mingle), GLm(Girard's linear logic with the mingle) and Lm (Lambek calculuswith restricted mingle).

cut-elimination Lambek calculus linear logic mingle rule