Abstract : We consider intuitionistic fragments of multiplicative linear logic for which we define appropriate notions of proof-nets. These are based on a correctness criterion that consists of decorating the nodes of a proof-structure with monoidal terms that must obey constraints reminiscent of phase semantics.
Philippe de Groote. An algebraic correctness criterion for intuitionistic multiplicative proof-nets. Theoretical Computer Science, Elsevier, 1999, 224 (1-2), pp.115-134. ⟨inria-00098817⟩