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An explicit formula for the free exponential modality of linear logic

Abstract : The exponential modality of linear logic associates a commutative comonoid !A to every formula A, in order to duplicate it. Here, we explain how to compute the free commutative comonoid !A in various models of linear logic, using a sequential limit of equalizers. The recipe is simple and elegant, and en- ables to unify for the first time the miscellaneous constructions of the exponential modality appearing in the literature. It also sheds light on the duplication policy of linear logic. We illustrate its relevance by applying it to three familiar models of linear logic based on coherence spaces, Conway games, and finiteness spaces.
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Preprints, Working Papers, ...
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Contributor : Nicolas Tabareau <>
Submitted on : Thursday, June 4, 2009 - 3:18:23 PM
Last modification on : Thursday, January 7, 2021 - 11:40:03 PM
Long-term archiving on: : Monday, October 15, 2012 - 11:46:22 AM


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  • HAL Id : hal-00391714, version 1




Paul-André Melliès, Nicolas Tabareau, Christine Tasson. An explicit formula for the free exponential modality of linear logic. 2009. ⟨hal-00391714v1⟩



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