Linear logic as a tool for reasoning on a Petri net model

The objective of this paper is to explore what could be the basis of a new approach for a model based diagnosis of discrete event dynamic systems such as manufacturing plants. The principle of this approach is to use linear logic in order to elaborate abductive reasonings above a Petri net based deep model of the behavior of the manufacturing system. In this paper we assume that the basis of a linear logic representation of a Petri net is known and we focus on the fact that a good utilization of the linear logic structural rules allows the direct characterization of sets of transition sequences. In other words the structural concurrency of a Petri net can be used at the reasoning level to generate sequences which only differ with respect to the firing order of parallel transitions. As a direct consequence of this result, the differences between the two multiplicative connectives ⊗ and ? of linear logic are stated. On the right part of the linear implication connective, the first one express the production of resources which have to be simultaneously consumed whereas the second one describes resources which can be independently consumed although they participate in a unique proof