Proof nets for unit-free multiplicative-additive linear logic (extended abstract)

A cornerstone of the theory of proof nets for unit-freemultiplicative linear logic (MLL) is the abstract representation of cut-freeproofs modulo inessential commutations of rules. The only knownextension to additives, based on monomial weights, fails topreserve this key feature: a host of cut-free monomial proof nets cancorrespond to the same cut-free proof. Thus the problem offinding a satisfactory notion of proof net for unit-freemultiplicative-additive linear logic (MALL) has remained open since theincep-tion of linear logic in 1986. We present a new definition of MALLproof net which remains faithful to the cornerstone of the MLLtheory.