Substructural logics with Mingle

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).
Keywords cut-elimination  Lambek calculus  linear logic  mingle rule
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Reprint years 2004
DOI 10.1023/A:1017586008091
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