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Communication Dans Un Congrès Mathematical Structures in Computer Science Année : 2018

An explicit formula for the free exponential modality of linear logic

Nicolas Tabareau
Christine Tasson
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Résumé

The exponential modality of linear logic associates a commutative comonoid !A to every formula A, this enabling to duplicate the formula in the course of reasoning. Here, we explain how to compute the free commutative comonoid !A as a sequential limit of equalizers in any symmetric monoidal category where this sequential limit exists and commutes with the tensor product. We apply this general recipe to a series of models of linear logic, typically based on coherence spaces, Conway games and niteness spaces. This algebraic description unies for the rst time the various constructions of the exponential modality in spaces and games. It also sheds light on the duplication policy of linear logic, and its interaction with classical duality and double negation completion.
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Dates et versions

hal-02436316 , version 1 (08-01-2021)

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Citer

Paul-André Melliès, Nicolas Tabareau, Christine Tasson. An explicit formula for the free exponential modality of linear logic. ICALP 2009 : 36th International Colloquium on Automata, Languages, and Programming, Jul 2009, Rhodes, Greece. pp.247-260, ⟨10.1007/978-3-642-02930-1_21⟩. ⟨hal-02436316⟩
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