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

Authors: 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}
  }