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Completeness of MLL proof-nets w.r.t. weak distributivity

Published online by Cambridge University Press:  12 March 2014

Jean-Baptiste Joinet
Affiliation:
EQUIPE Preuves-Programmes-SystÈmes, CNRS - UniversitÉ, Paris 7 (UMR 7126), Case 7014, 2 Place Jussieu, F-75251 Paris Cedex 05, France. E-mail: joinet@pps.jussieu.fr URL: www-philo.univ-parisl.fr/Joinet
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Abstract

We examine ‘weak-distributivity’ as a rewriting rule defined on multiplicative proofstructures (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 : starting from a set of simple generators (proof-nets which are a n-ary ⊗ of Ց-ized axioms), any mono-conclusion MLL proof-net can be reached by rewriting (up to ⊗ and Ց associativity and commutativity).

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2007

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References

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