Proof Nets for Unit-free Multiplicative-Additive Linear Logic

Joint work with Dominic Hughes
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 rule commutation. 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.

Warning:
This is not an introduction to Linear Logic. The talk may have the character of an informal explanation of my work in this area for a small group of people interested in abstractions of proofs.

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Last updated by tbourke at Fri Nov 26 19:00:03 2004 GMT+1100