Modules in Non-commutative Logic

The question we want to investigate was expressed by Girard in [3]: “Assume that I am given a program P [a proof-net II], and that I cut it in two parts arbitrarily. I create two ... modules, linked together by their border. Can I express that my two modules are complementary [orthogonal], in other terms that I can branch them by identification over their common border? One would like to define the type of the modules as their branching instructions; these branching instructions should be such that they authorized the restoring of the original P [the proof-net II].”