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ACS
2005

Relating Categorical Semantics for Intuitionistic Linear Logic

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Relating Categorical Semantics for Intuitionistic Linear Logic
There are several kinds of linear typed calculus in the literature, some with their associated notion of categorical model. Our aim in this paper is to systematise the relationship between three of these linear typed calculi and their models. We point out that mere soundness and completeness of a linear typed calculus with respect to a class of categorical models are not sufficient to identify the most appropriate class uniquely. We recommend instead to use the notion of internal language when relating a typed calculus to a class of models. After clarifying the internal languages of the categories of models in the literature we relate these models via reflections and coreflections. Key words: intuitionistic linear logic, typed lambda calculus, symmetric monoidal closed categories, symmetric monoidal adjunctions. AMS classifications: 03G30 03B15 18C50 03B20
Maria Emilia Maietti, Paola Maneggia, Valeria de P
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2005
Where ACS
Authors Maria Emilia Maietti, Paola Maneggia, Valeria de Paiva, Eike Ritter
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