Paper: Cut Elimination for Monomial MALL Proof Nets (at LICS 2008)

Authors: Olivier Laurent Roberto Maieli

Abstract

We present a syntax for MALL (multiplicative additive linear logic without units) proof nets which refines Girard's one. It is also based on the use of monomial weights for identifying additive components (slices). Our generalization gives the possibility of representing a kind of sharing of nodes which does not exist in Girard's nets. This sharing leads to the definition of a strong cut elimination procedure for MALL. We give a correctness criterion which is proved to be stable by reduction and to give a sequentialization theorem with respect to the sequent calculus. Sequentialization is proved by showing that an expansion procedure allows us to unfold any of our proof nets into a Girard proof net.

BibTeX

  @InProceedings{LaurentMaieli-CutEliminationforMo,
    author = 	 {Olivier Laurent and Roberto Maieli},
    title = 	 {Cut Elimination for Monomial MALL Proof Nets},
    booktitle =  {Proceedings of the Twenty-Third Annual IEEE Symposium on Logic in Computer Science (LICS 2008)},
    year =	 {2008},
    month =	 {June}, 
    pages =      {486--497},
    location =   {Pittsburgh, PA, USA}, 
    publisher =	 {IEEE Computer Society Press}
  }