Loose Semantics of Petri Nets

In this paper, we propose a new,loose semantics for place/transition nets based on transition systems and generalizing the reachability graph semantics. The loose semantics of a place/transition net reflects all its possible refinements and is given as a category of transition systems with alternative sequences of events over the net. The main result states that each plain morphism between two place/transitions nets induces a free construction between the corresponding semantic categories.