Substructural logics with Mingle

Journal of Logic, Language and Information 11 (2):227-249 (2002)
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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).

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2004

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10.1023/a:1017586008091

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Citations of this work

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References found in this work

Proof theory.Gaisi Takeuti - 1975 - New York, N.Y., U.S.A.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co..
The Mathematics of Sentence Structure.Joachim Lambek - 1958 - Journal of Symbolic Logic 65 (3):154-170.
Semantics for relevant logics.Alasdair Urquhart - 1972 - Journal of Symbolic Logic 37 (1):159-169.
Lectures on Linear Logic.Anne Sjerp Troelstra - 1992 - Center for the Study of Language and Information Publications.
Extending intuitionistic linear logic with knotted structural rules.R. Hori, H. Ono & H. Schellinx - 1994 - Notre Dame Journal of Formal Logic 35 (2):219-242.

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