The Structure of Exponentials : Uncovering the Dynamics of Linear

We construct the exponential graph of a proof in (second order) linear logic, an artefact displaying the interdependencies of ex-ponentials in. Within this graph superruous exponentials are deened, the removal of which is shown to yield a correct proof. with essentially the same set of reductions. Applications to intuitionistic and classical proofs are given by means of reduction-preserving embeddings into linear logic. The last part of the paper puts things the other way round, and deenes families of linear logics in which exponential dependencies are ruled by a given graph. We sketch some work in progress and possible applications.