An explicit formula for the free exponential modality of linear logic

Paul-André Melliès (1) , Nicolas Tabareau (1) , Christine Tasson (1)

1 PPS - Preuves, Programmes et Systèmes

The exponential modality of linear logic associates a commutative comonoid !A to every formula A, in order to duplicate it. Here, we explain how to compute the free commutative comonoid !A in various models of linear logic, using a sequential limit of equalizers. The recipe is simple and elegant, and en- ables to unify for the first time the miscellaneous constructions of the exponential modality appearing in the literature. It also sheds light on the duplication policy of linear logic. We illustrate its relevance by applying it to three familiar models of linear logic based on coherence spaces, Conway games, and finiteness spaces.

Domaines: Catégories et ensembles [math.CT]; Logique en informatique [cs.LO]

Paul-André Melliès, Nicolas Tabareau, Christine Tasson. An explicit formula for the free exponential modality of linear logic. 2009. ⟨hal-00391714v1⟩