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Quantales as completions of ordered monoids: revised semantics for Intuitionistic Linear Logic

Didier Galmiche 1 Dominique Larchey-Wendling 1
1 TYPES - Logic, proof Theory and Programming
LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The aim of this paper is to propose a unified analysis of the relationships between the notions of order and closure and to relate it to different semantics of Intuitionistic Linear Logic (ILL). We study the embedding of ordered monoids into quantales and then we propose general constructions and results about such an embedding. Therefore we obtain a new semantics based on ordered monoids and also new completeness results for ILL.
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https://hal.inria.fr/inria-00099226
Contributor : Publications Loria <>
Submitted on : Tuesday, September 26, 2006 - 8:52:00 AM
Last modification on : Friday, February 26, 2021 - 3:28:08 PM

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  • HAL Id : inria-00099226, version 1

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Didier Galmiche, Dominique Larchey-Wendling. Quantales as completions of ordered monoids: revised semantics for Intuitionistic Linear Logic. Electronic Notes in Theoretical Computer Science, Elsevier, 2000, 35, 15 p. ⟨inria-00099226⟩

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