I will first introduce linear logic proof nets, for the multiplicative and exponential fragment (MELL), and I will especially insist on the computational meaning of the exponential boxes: these are constructions containing the possibility of duplication and deletion of entire parts of the structures (all the non linear part of the calculus).

Once these notions are introduced, I will explain how it is possible to express this computational paradigm in a linear setting through a syntactical Taylor expansion. The idea is to understand exponential boxes in a differential variant of linear logic, and to represent it with linear combination.

If we have time, I will try to give an idea of some algebraic issues concerning this construction, and a method to show for example, that the normal form of the Taylor expansion of a MELL always converges.

NB: Taylor expansion is here analogical to the lambda calculus (with its differential version too) one, if someone heard about it, it can give a first intuition.