A Correspondence between Maximal Abelian Sub-Algebras and Linear Logic Fragments
نویسنده
چکیده
We show a correspondence between a classification of maximal abelian sub-algebras (MASAs) proposed by Jacques Dixmier (Dix54) and fragments of linear logic. We expose for this purpose a modified construction of Girard’s hyperfinite geometry of interaction (Gir11). 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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عنوان ژورنال:
- Mathematical Structures in Computer Science
دوره 28 شماره
صفحات -
تاریخ انتشار 2018