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

An introduction to Differential Linear Logic: proof-nets, models and antiderivatives