We investigate a new denotational model of linear logic based on the purely relational model. In this semantics, webs are equipped with a notion of \\nitary" subsets, satisfying a closure condition with respect to an orthogonality relation between subsets of the web, and proofs are interpreted by nitary sets. This model seems quite diierent in spirit from… (More)
Models of the untyped λ-calculus may be defined either as applicative structures satisfying a bunch of first order axioms, known as " λ-models " , or as (structures arising from) any reflexive object in a cartesian closed category (ccc, for brevity). These notions are tightly linked in the sense that: given a λ-model A, one may define a ccc in which A (the… (More)
A general category of games is constructed, adapting and extending 1, 2]. Then, a sub-category of saturated strategies, closed under all possible codings in copy games, is shown to model reduction in classical Linear Logic.
We show that the extensional collapse of the relational model of linear logic is the model of prime-algebraic complete lattices, a natural extension to linear logic of the well known Scott semantics of the lambda-calculus.