From Proof nets to the Free *-Autonomous Categories

François Lamarche 1 Lutz Strassburger 1
1 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the well-known theory of unit-free multiplicative proof nets. A linking is no longer a set of axiom links but a tree in which the axiom links are subtrees. These trees will be identified according to an equivalence relation based on a simple form of graph rewriting. We show the standard results of sequentialization and strong normalization of cut elimination. In the second part of the paper we show that the identifications enforced on proofs are such that the class of two-conclusion proof nets defines the free *-autonomous category.
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Submitted on : Thursday, November 16, 2006 - 2:41:52 PM
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François Lamarche, Lutz Strassburger. From Proof nets to the Free *-Autonomous Categories. Logical Methods in Computer Science, Logical Methods in Computer Science Association, 2006, 2 (4:3), 44 p. ⟨10.2168/LMCS-2(4:3) 2006⟩. ⟨inria-00099865v2⟩

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