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A natural deduction and its corresponding sequent calculus for positive contraction-less relevant logic

Ilić M.

Reports on Mathematical Logic

2017

Vol. 52

101--132

We give a normalizing system of natural deduction for positive contraction-less relevant logic RW+⁰ . The specific characteristic of our calculus is that it has a simple translational relationship to a particular sequent calculus for RW+⁰, such that normal natural deduction derivations correspond to cut-free sequent calculus derivations and vice versa. By translations from natural deduction to sequent calculus derivations, and back, together with cut-elimination, we obtain an indirect proof of the normalization.