An introduction to differential linear logic: proof-nets, models and antiderivatives

Abstract

Differential linear logic enriches linear logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for differential linear logic and a categorical axiomatization of its denotational models. We also introduce a simple categorical condition on these models under which a general antiderivative operation becomes available. Last, we briefly describe the model of sets and relations and give a more detailed account of the model of finiteness spaces and linear and continuous functions.