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March 2007 Completeness of MLL proof-nets w.r.t. weak distributivity
Jean-Baptiste Joinet
J. Symbolic Logic 72(1): 159-170 (March 2007). DOI: 10.2178/jsl/1174668390

Abstract

We examine ‘weak-distributivity’ as a rewriting rule $\underset{\leadsto{}}{WD}$ defined on multiplicative proof-structures (so, in particular, on multiplicative proof-nets: MLL). This rewriting does not preserve the type of proof-nets, but does nevertheless preserve their correctness. The specific contribution of this paper, is to give a direct proof of completeness for $\underset{\leadsto{}}{WD}$: starting from a set of simple generators (proof-nets which are a $n$-ary $\otimes$ of $\parr$-ized axioms), any mono-conclusion MLL proof-net can be reached by $\underset{\leadsto{}}{WD}$ rewriting (up to $\otimes$ and $\parr$ associativity and commutativity).

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Jean-Baptiste Joinet. "Completeness of MLL proof-nets w.r.t. weak distributivity." J. Symbolic Logic 72 (1) 159 - 170, March 2007. https://doi.org/10.2178/jsl/1174668390

Information

Published: March 2007
First available in Project Euclid: 23 March 2007

zbMATH: 1121.03083
MathSciNet: MR2298477
Digital Object Identifier: 10.2178/jsl/1174668390

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 1 • March 2007
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