Denotational Semantics for Propositional Light Affine Logic

Denotational semantics often make invariants explicit which are implicit in the structure of a proof theoretic system. Asperti’s Light Affine Logic is a proof theoretic system, which can be viewed as a computation model. It was shown by Asperti and Roversi that, as a computation model, it captures the feasible functions. Light Affine Logic is a simplification of Girard’s Light Linear Logic, to which full weakening is added. Baillot presented in 2004 a model for the propositional fragment of Light Linear Logic. We adopt Baillot’s model to the propositional fragment of Light Affine Logic by taking full weakening into account. For this sake, we present Terui’s untyped term calculus λLA, a fragment of which is typable with the Light Affine type system. The Light Affine type system is Light Affine Logic translated via the Curry-Howard correspondence.