## Paper: Proof Nets for Unit-free Multiplicative-Additive Linear Logic (Extended abstract) (at LICS 2003)

**Dominic J. D. Hughes Rob J. van Glabbeek**

### Abstract

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 incep-tion of linear logic in 1986. We present a new definition of MALL proof net which remains faithful to the cornerstone of the MLL theory.

### BibTeX

@InProceedings{HughesvanGlabbeek-ProofNetsforUnitfre, author = {Dominic J. D. Hughes and Rob J. van Glabbeek}, title = {Proof Nets for Unit-free Multiplicative-Additive Linear Logic (Extended abstract)}, booktitle = {Proceedings of the Eighteenth Annual IEEE Symposium on Logic in Computer Science (LICS 2003)}, year = {2003}, month = {June}, pages = {1--10}, location = {Ottawa, Canada}, publisher = {IEEE Computer Society Press} }