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arXiv · 1408.2125

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

Thomas Seiller
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Abstract

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.

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Thomas Seiller. 2015-09-23. A Correspondence between Maximal Abelian Sub-Algebras and Linear Logic Fragments. https://doi.org/10.1017/s0960129516000062

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