A categorical linear framework for Petri nets

This research brings together, in a methodical way, several approaches to giving a compositional theory of Petri nets using category theory and to the use of linear logic in specifying and reasoning about Petri nets. The authors construct categories of nets based on V.C.V. de Paiva´s dialectica category models (1989) of linear logic in which they are able to exploit the structure of de Paiva´s models to give constructions on categories of nets. Using a category of safe nets as an example, it is shown how this approach yields both existing and novel constructions on nets and their computational interpretation is discussed. The authors also indicate how more general categories of nets can be expressed in this framework