Conflict nets: Efficient locally canonical MALL proof nets - Hughes, Dominic; Heijltjes, Willem (Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, 2016)
Proof nets for MLL (unit-free multiplicative linear logic) and ALL (unit-free additive linear logic) are graphical abstractions of proofs which are efficient (proofs translate in linear time) and canonical (invariant under rule commutation). This paper solves a three-decade open problem: are there efficient canonical proof nets for MALL (unit-free multiplicative-additive linear logic)? Honouring MLL and ALL canonicity, in which all commutations are strictly local proof-tree rewrites, we define local canonicity for MALL: invariance under local rule commutation. We present new proof nets for MALL, called conflict nets, which are both efficient and locally canonical.