From ordered monoids to quantales and Petri nets: completeness results revisited in Intuitionistic Linear Logic
Résumé
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.