Theoretical Computer Science
Theoretical Computer Science - International Joint Conference on Theory and Practice of Software Development, P
Games and full completeness for multiplicative linear logic
Journal of Symbolic Logic
Concurrent Games and Full Completeness
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Locus Solum: From the rules of logic to the logic of rules
Mathematical Structures in Computer Science
Asynchronous Games 4: A Fully Complete Model of Propositional Linear Logic
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
A Neutral Approach to Proof and Refutation in MALL
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
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In the standard sequent presentations of Girard's Linear Logic [Girard, J.-Y., Linear logic, Theoretical Computer Science 50 (1987), pp. 1-102] (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.