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Linear Logic on Petri Nets.

Engberg, U.; Winskel, G.

In: de Bakker, J.W.; de Roever, W.-P.; Rozenberg, G.: Lecture Notes in Computer Science, Vol. 803; A Decade of Concurrency, pages 176-229. Springer-Verlag, June 1993.

Abstract: This article shows how individual Petri nets form models of Girard's intuitionistic linear logic. It explores questions of expressiveness and completeness of linear logic with respect to this interpretation. An aim is to use Petri nets to give an understanding of linear logic and give some appraisal of the value of linear logic as a specification logic for Petri nets. This article might serve as a tutorial, providing one in-road into Girard's linear logic via Petri nets. With this in mind we have added several exercises and their solutions. We have made no attempt to be exhaustive in our treatment, dedicating our treatment to one semantics of intuitionistic linear logic. Completeness is shown for several versions of Girard's linear logic with respect to Petri nets as the class of models. The strongest logic considered is intuitionistic linear logic. This logic is shown sound and complete with respect to atomic nets (this include nets in which every transition leads to a nonempty multiset of places). The logic is remarkably expressive, enabling descriptions of the kinds of properties one might wish to show of nets; in particular, negative properties, asserting the impossibility of an assertion, can also be expressed. A start is made on decidability issues.

Keywords: Linear logic; Petri nets.

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