Geometry of Interaction V: Logic in the hyperfinite factor

Jean-Yves Girard (1)

1 IML - Institut de mathématiques de Luminy

Geometry of Interaction is a transcendental syntax developed in the framework of operator algebras. This fifth installment of the program takes place inside a von Neumann algebra, the hyperfinite factor. It provides a built-in interpretation of cut-elimination as well as an explanation for light, i.e., complexity sensitive, logics.

Mots clés: proof-theory; linear logic; complexity theory; light logics; operator algebras

Domaines: Logique [math.LO]

Jean-Yves Girard. Geometry of Interaction V: Logic in the hyperfinite factor. Theoretical Computer Science, 2011, Girard’s Festschrift, 412 (20), pp.1860-1883. ⟨10.1016/j.tcs.2010.12.016⟩. ⟨hal-01322171⟩