## Petri Nets as Quantales

**Carolyn Brown**
*Abstract:* This paper brings together two areas of
interest in linear logic. It is known that proof in linear logic
corresponds to evolution of Petri nets in a precise way, and also
that quantales are an algebraic model of linear logic. We here show
how a Petri net can be used to generate a quantale whose structure
reflects the behaviour of the net. Such a net-quantale can then be
used to give a sound interpretation of the linear logic proof
rules. This interpretation allows us to specify properties of nets.
The sorts of properties we can specify may be possibilities, which
are expressed using implication, or impossibilities (safety
properties, in effect), which are expressed using negation. The
quantale also gives rise to an equivalence on nets.

*ECS-LFCS-89-96*

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