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A correspondence between maximal abelian sub-algebras and linear logic fragments

Published online by Cambridge University Press:  28 July 2016

THOMAS SEILLER
THOMAS SEILLER*
Affiliation:
I.H.É.S., Le Bois-Marie, 35, Route de Chartres, 91440 Bures-sur-Yvette, France Email: seiller@ihes.fr
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Abstract

We show a correspondence between a classification of maximal abelian sub-algebras (MASAs) proposed by Jacques Dixmier (Dixmier 1954. Annals of Mathematics59 (2) 279–286) and fragments of linear logic. We expose for this purpose a modified construction of Girard's hyperfinite geometry of interaction (Girard 2011. Theoretical Computer Science412 (20) 1860–1883). The expressivity of the logic soundly interpreted in this model is dependent on properties of a MASA which is a parameter of the interpretation. We also unveil the essential role played by MASAs in previous geometry of interaction constructions.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Issue 1 , January 2018 , pp. 77 - 139
Copyright
Copyright © Cambridge University Press 2016 

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