The Semantics and Proof Theory of Linear Logic

Theoretical Computer Science 57:161-184 (1988)
Linear logic is a new logic which was recently developed by Girard in order to provide a logical basis for the study of parallelism. It is described and investigated in Gi]. Girard's presentation of his logic is not so standard. In this paper we shall provide more standard proof systems and semantics. We shall also extend part of Girard's results by investigating the consequence relations associated with Linear Logic and by proving corresponding str ong completeness theorems. Finally, we shall investigate the relation between Linear Logic and previously known systems, especially Relevance logics
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Heinrich Wansing & Graham Priest (2015). External Curries. Journal of Philosophical Logic 44 (4):453-471.
Arnon Avron (2014). What is Relevance Logic? Annals of Pure and Applied Logic 165 (1):26-48.

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