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Exploring the Gap between Linear and Classical Logic

François Lamarche 1
1 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The Medial rule was first devised as a deduction rule in the Calculus of Structures. In this paper we explore it from the point of view of category theory, as additional structure on a *-autonomous category. This gives us some insights on the denotational semantics of classical propositional logic, and allows us to construct new models for it, based on suitable generalizations of the theory of coherence spaces.
Keywords : Bialgebras Linear Logic Classical Logic -autonomous Categories Denotational Semantics Coherence Spaces Deep Inference Medial Rule Bialgebras.
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https://hal.inria.fr/inria-00113785
Contributor : Francois Lamarche <>
Submitted on : Wednesday, November 14, 2007 - 4:00:30 PM
Last modification on : Thursday, January 11, 2018 - 6:19:48 AM
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François Lamarche. Exploring the Gap between Linear and Classical Logic. Theory and Applications of Categories, Mount Allison University, 2007, 18 (17), 473--535 (63 p.). ⟨inria-00113785⟩

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