Categorical models of Linear Logic with fixed points of formulas

Thomas Ehrhard (1) , Farzad Jafarrahmani (2)

1 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
2 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

We develop a denotational semantics of Linear Logic with least and greatest fixed points in a general categorical setting based on the notion of Seely category and on strong functors acting on them. We exhibit a simple instance of this setting in the category of sets and relations, where least and greatest fixed points are interpreted in the same way, and in a category of sets equipped with a notion of totality (non-uniform totality spaces) and relations preserving them, where least and greatest fixed points have distinct interpretations.

Domaines: Logique en informatique [cs.LO]

Thomas Ehrhard, Farzad Jafarrahmani. Categorical models of Linear Logic with fixed points of formulas. 2020. ⟨hal-03013356v1⟩