Abstract
In this paper we 1. provide a natural deduction system for full first-order linear logic, 2. introduce Curry-Howard-style terms for this version of linear logic, 3. extend the notion of substitution of Curry-Howard terms for term variables, 4. define the reduction rules for the Curry-Howard terms and 5. outline a proof of the strong normalization for the full system of linear logic using a development of Girard's candidates for reducibility, thereby providing an alternative to Girard's proof using proof-nets.
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Bäuerle, F.A., Albrecht, D., Crossley, J.N. et al. Curry-Howard Terms for Linear Logic. Studia Logica 61, 223–235 (1998). https://doi.org/10.1023/A:1005025414656
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DOI: https://doi.org/10.1023/A:1005025414656