The Semantics and Proof Theory of Linear Logic
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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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Edwin Mares & Francesco Paoli (2014). Logical Consequence and the Paradoxes. Journal of Philosophical Logic 43 (2-3):439-469.
Heinrich Wansing (1993). Informational Interpretation of Substructural Propositional Logics. Journal of Logic, Language and Information 2 (4):285-308.
Glyn Morrill (1990). Intensionality and Boundedness. Linguistics and Philosophy 13 (6):699 - 726.
Arnon Avron (2014). What is Relevance Logic? Annals of Pure and Applied Logic 165 (1):26-48.
Johan Benthem (1991). Language in Action. Journal of Philosophical Logic 20 (3):225 - 263.
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