A semantics for priority using partial orders with a simultaneity relation

In this paper we present a semantics for concurrent systems with priority constraints, using as a basis partial orders of events with both precedence and simultaniety relations. Previous work has shown that theories based on partial orders modelling precedence alone are insufficient to capture priority. We use the prosset model of Gaifman and Pratt, an extension to partial-order theories which includes a relation for explicity simultaneity, to develop a semantics for a COSY dialect allowing the specification of priority. We show that Janicki's "sequences of multiples" semantics for priorities can be derived from a linearization of the prosset semantics. Finally, we look at a simple taxonomy to clarify the relation of these various semantics to other event-history models.