Resource modalities in tensor logic

Paul-André Melliès, Nicolas Tabareau
2010 Annals of Pure and Applied Logic  
The description of resources in game semantics has never achieved the simplicity and precision of linear logic, because of the misleading conception that linear logic is more primitive than game semantics. Here, we defend the opposite view, and thus advocate that game semantics is conceptually more primitive than linear logic. This revised point of view leads us to introduce tensor logic, a primitive variant of linear logic where negation is not involutive. After formulating its categorical
more » ... ntics, we interpret tensor logic in a model based on Conway games equipped with a notion of payoff, in order to reflect the various resource policies of the logic: linear, affine, relevant or exponential.
doi:10.1016/j.apal.2009.07.018 fatcat:4jqktwfiava3lhfi7ay47kj7lq