Categorical models of linear logic revisited

Paul-André Melliès (1)

1 PPS - Preuves, Programmes et Systèmes

In this survey, we review the existing categorical axiomatizations of linear logic, with a special emphasis on Seely and Lafont presentations. In a first part, we explain why Benton, Bierman, de Paiva and Hyland had to replace Seely categories by a more complicated axiomatization, and how a while later, Benton managed to simplify this axiomatization. In a second part, we show how Lafont axiomatization may be relaxed, in order to admit exponential interpretations different from the free one. Finally, we illustrate with a few examples what categorical models can teach us about linear logic and its models.

Mots clés: Linear logic; categories; coherence space

Domaines: Logique en informatique [cs.LO]

Paul-André Melliès. Categorical models of linear logic revisited. 2003. ⟨hal-00154229⟩