Interactive correctness criterion for multiplicative-additive proof-nets

Proof-nets are special graphs (proof-structures) representing desequentialised proofs of the linear logic sequent calculus. Each proof-net stands for a class of sequent proofs which are equivalent modulo irrelevant permutations of logical rules. Here we present an interactive characterisation of those cut-free proof-structures coming from proofs of the multiplicative-additive fragment of linear logic (MALL, see [1, 3]). This work is intended to extend to MALL proof-nets an original proposal for an interactive correction criterion for proof-nets of the multiplicative fragment of linear logic. Its natural consequence we will be the study of the question of modularity for additive proof-nets