We introduce a new class of multiplicative proof nets, J-proof nets,which are a typed version of Faggian and Maurel's multiplicative L-nets.In J-proof nets,we can characterize nets with different degrees of sequentiality, by gradual insertion of sequentiality constraints. As a byproduct, we obtain a simple proof of the sequentialisation theorem.
DI GIAMBERARDINO, P., Faggian, C. (2006). Jump from parallel to sequential proofs: multiplicatives.. In Lecture Notes in Computer Science 4207 (pp.319-333). Berlin Heidelberg : Springer Verlag.