A normalizing system of natural deduction for intuitionistic linear logic

Archive for Mathematical Logic 41 (8):789-810 (2002)
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Abstract

The main result of this paper is a normalizing system of natural deduction for the full language of intuitionistic linear logic. No explicit weakening or contraction rules for -formulas are needed. By the systematic use of general elimination rules a correspondence between normal derivations and cut-free derivations in sequent calculus is obtained. Normalization and the subformula property for normal derivations follow through translation to sequent calculus and cut-elimination

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Bilateralism in Proof-Theoretic Semantics.Nissim Francez - 2014 - Journal of Philosophical Logic 43 (2-3):239-259.
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References found in this work

Varieties of linear calculi.Sara Negri - 2002 - Journal of Philosophical Logic 31 (6):569-590.
Normal deduction in the intuitionistic linear logic.G. Mints - 1998 - Archive for Mathematical Logic 37 (5-6):415-425.

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