Resource modalities in tensor logic

Abstract : The description of resources in game semantics has never achieved the simplicity and precision of linear logic, because of a misleading conception: the belief that linear logic is more primitive than game semantics. We advocate instead the contrary: that game semantics is conceptually more primitive than linear logic. Starting from this revised point of view, we design a categorical model of resources in game semantics, and construct a Conway game model extended with a notion of payoff in order to capture various resource policies: linear, affine, relevant and exponential.
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Paul-André Melliès, Nicolas Tabareau. Resource modalities in tensor logic. Annals of Pure and Applied Logic, Elsevier Masson, 2010, 161 (5), pp.632-653. ⟨10.1016/j.apal.2009.07.018⟩. ⟨hal-00339154v2⟩

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