Probabilistic Event Structures and Domains

We investigate probability in the presence of causal dependence and independence. More precisely, we study the process model of probabilistic event structures. We characterise the “global valuation” induced on the configurations by a probabilistic event structure and show how global valuations restrict to probability distributions on certain “test” sets. This leads to a definition of probabilistic runs and a proof of their confluence. A special case of confluence is established via a form of Markov decision process. Finally, we show how probabilistic event structures correspond to certain elements of the probabilistic powerdomain of the domain of configurations of the event structure.