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

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.

Mots clés: semantics; quantales; linear logic; completeness; logique lineaire; completude; preuves; proofs; semantique

Domaines: Autre [cs.OH]

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⟩