On Causality Semantics of Nets with Priorities

In the formal treatment of concurrent computing systems, causality and weak causality can be used to provide abstract specifications of the temporal ‘earlier than’ and ‘not later than’ orderings. In this paper we consider relational structures comprising causality and weak causality — called stratified order structures — which can be used to provide a non-sequential semantics of Petri nets with inhibitor arcs. We show that this approach can be extended to nets augmented with priority specifications. In particular, we demonstrate how to derive stratified order structures for such nets by generalising the standard construction of causal partial orders based on occurrence nets.