Can I read A Correspondence between Maximal Abelian Sub-Algebras and Linear Logic Fragments on EtoBox?

A Correspondence between Maximal Abelian Sub-Algebras and Linear Logic Fragments by Seiller, Thomas is a scholarly article available to read on EtoBox.

What is A Correspondence between Maximal Abelian Sub-Algebras and Linear Logic Fragments about?

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.

Author

Seiller, Thomas

Published

2014

Language

EN