Dominic Hughes - Selected Papers

Proof Nets for unit-free Multiplicative-Additive Linear Logic (Extended abstract) [FAQ - Slides - pdf - ps - ps.gz - tex - bibtex] footnote.
With Rob van Glabbeek as second author.
Logic in Computer Science, 2003.

A cornerstone of the theory of proof nets for unit-free multiplicative linear logic (MLL) is the abstract representation of cut-free proofs modulo inessential commutations of rules. The only known extension to additives, based on monomial weights, fails to preserve this key feature: a host of cut-free monomial proof nets can correspond to the same cut-free proof. Thus the problem of finding a satisfactory notion of proof net for unit-free multiplicative-additive linear logic (MALL) has remained open since the inception of linear logic in 1986. We present a new definition of MALL proof net which remains faithful to the cornerstone of the MLL theory.