A geometrical procedure for computing relaxation

Annals of Pure and Applied Logic 158 (1-2):80-89 (2009)
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Abstract

Permutative logic is a non-commutative conservative extension of linear logic suggested by some investigations on the topology of linear proofs. In order to syntactically reflect the fundamental topological structure of orientable surfaces with boundary, permutative sequents turn out to be shaped like q-permutations. Relaxation is the relation induced on q-permutations by the two structural rules divide and merge; a decision procedure for relaxation has been already provided by stressing some standard achievements in theory of permutations. In these pages, we provide a parallel procedure in which the problem at issue is approached from the point of view afforded by geometry of 2-manifolds and solved by making specific surfaces interact

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10.1016/j.apal.2008.10.008

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Gabriele Pulcini
University of Campinas

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References found in this work

Quantales and (noncommutative) linear logic.David N. Yetter - 1990 - Journal of Symbolic Logic 55 (1):41-64.
Linear logic: its syntax and semantics.Jean-Yves Girard - 1995 - In Jean-Yves Girard, Yves Lafont & Laurent Regnier (eds.), Advances in linear logic. New York, NY, USA: Cambridge University Press. pp. 222--1.
Non-commutative logic I: the multiplicative fragment.V. Michele Abrusci & Paul Ruet - 1999 - Annals of Pure and Applied Logic 101 (1):29-64.
Non-commutative logic I: the multiplicative fragment.P. Ruet & M. Abrusci - 1999 - Annals of Pure and Applied Logic 101 (1):29-64.
Planar and braided proof-nets for multiplicative linear logic with mix.G. Bellin & A. Fleury - 1998 - Archive for Mathematical Logic 37 (5-6):309-325.

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