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arXiv · 0905.4064

Contraction-free proofs and finitary games for Linear Logic

André Hirschowitz·Michel Hirschowitz·Tom Hirschowitz
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Abstract

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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André Hirschowitz, Michel Hirschowitz, Tom Hirschowitz. 2009-05-25. Contraction-free proofs and finitary games for Linear Logic. https://doi.org/10.1016/j.entcs.2009.07.095

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