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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Eunsuk Yang (2013). R and Relevance Principle Revisited. Journal of Philosophical Logic 42 (5):767-782.
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