Process semantics of general inhibitor nets

We define a causality semantics of Place/Transition nets with weighted inhibitor arcs (PTI-nets). We extend the standard approach to defining the partial order semantics of Place/Transition nets (PT-nets) based on the process semantics given through occurrence nets. To deal with inhibitor arcs at the level of occurrence nets activator arcs (and extra conditions) are used. The properties of the resulting activator occurrence nets are extensively investigated. It is then demonstrated how processes corresponding to step sequences of PTI-nets can be constructed algorithmically, and a non-algorithmic (axiomatic) characterisation is given of all those processes that can be obtained in this way. In addition, a general framework is established allowing to separately discuss behaviour, processes, causality, and their properties before proving that the resulting notions are mutually consistent for the various classes of Petri nets considered. This facilitates an efficient and uniform presentation of our results.