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arXiv:1408.2125 [math.LO]AbstractReferencesReviewsResources

A Correspondence between Maximal Abelian Sub-Algebras and Linear Logic Fragments

Thomas Seiller

Published 2014-08-09, updated 2015-09-23Version 2

We show a correspondence between a classification of maximal abelian sub-algebras (MASAs) proposed by Jacques Dixmier and fragments of linear logic. We expose for this purpose a modified construction of Girard's hyperfinite geometry of interaction which interprets proofs as operators in a von Neumann algebra. 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.

Categories: math.LO, cs.LO
Subjects: 03B70, 03F52, 03B47, 47N99, 46L99
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