Gruppo di Logica e Geometria della Cognizione

Implicative Algebras were recently introduced by Alexandre Miquel as a unified framework for forcing and realisability, whose particularity is to interpret terms and formulæ uniformly. In this ongoing work, we show how linear logic fits in this picture: we present a notion of model of intuitionistic linear logic in which sits both syntactic models and a localized phase semantics ; and show how to transform such a model into an algebra allowing to interpret faithfully all the connectives of classical linear logic.