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From ordered monoids to quantales and Petri nets: completeness results revisited in 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 : This paper presents a new semantics of Intuitionistic Linear Logic and its relationships with Petri nets. It comes from a new analysis of the links between ordered monoids, quantales and Petri nets. The main results are: a new completeness result for ILL from a new interpretation of the logic on nets and also a finite model property, that means completeness w.r.t finite quantales or Petri nets.
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https://hal.inria.fr/inria-00098530
Contributor : Publications Loria <>
Submitted on : Monday, September 25, 2006 - 5:03:10 PM
Last modification on : Friday, February 26, 2021 - 3:28:08 PM

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  • HAL Id : inria-00098530, version 1

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Didier Galmiche, Dominique Larchey-Wendling. From ordered monoids to quantales and Petri nets: completeness results revisited in Intuitionistic Linear Logic. Workshop on Domains IV, 1998, Rolandseck, Germany. ⟨inria-00098530⟩

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