Contraction-free proofs and finitary games for Linear Logic

Details Contraction-free proofs and finitary games for Linear Logic Contraction-free proofs and finitary games for Linear Logic

2009-05-25

arxiv.org/abs/0905.4064v1

MFPS 2009, Oxford : Royaume-Uni (2009)

Computer Science

Logic in Computer Science

19 pages, uses tikz and Paul Taylor's diagrams

Scientific paper

10.1016/j.entcs.2009.07.095

In the standard sequent presentations of Girard's Linear Logic (LL), there are two "non-decreasing" rules, where the premises are not smaller than the conclusion, namely the cut and the contraction rules. It is a universal concern to eliminate the cut rule. We show that, using an admissible modification of the tensor rule, contractions can be eliminated, and that cuts can be simultaneously limited to a single initial occurrence. This view leads to a consistent, but incomplete game model for LL with exponentials, which is finitary, in the sense that each play is finite. The game is based on a set of inference rules which does not enjoy cut elimination. Nevertheless, the cut rule is valid in the model.

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