Abstract.
We describe a natural deduction system NDIL for the second order intuitionistic linear logic which admits normalization and has a subformula property. NDIL is an extension of the system for !-free multiplicative linear logic constructed by the author and elaborated by A. Babaev. Main new feature here is the treatment of the modality !. It uses a device inspired by D. Prawitz' treatment of S4 combined with a construction \(<\Gamma>\) introduced by the author to avoid cut-like constructions used in \(\otimes\)-elimination and global restrictions employed by Prawitz. Normal form for natural deduction is obtained by Prawitz translation of cut-free sequent derivations.
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Received: March 29, 1996
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Mints, G. Normal deduction in the intuitionistic linear logic. Arch Math Logic 37, 415–425 (1998). https://doi.org/10.1007/s001530050106
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DOI: https://doi.org/10.1007/s001530050106