Abstract

This paper investigates probability in the presence of causal dependence. More precisely, it studies the process model of probabilistic event structures. In their simplest form probabilistic choice is localised to cells at which immediate conflict arises; in which case probabilistic independence coincides with causal independence. An event structure is associated with a domain—that of its configurations ordered by inclusion. In domain theory probabilistic processes are denoted by continuous valuations on a domain. A key result of this paper is a representation theorem showing how continuous valuations on the domain of a confusion free event structure correspond to the probabilistic event structures it supports. Via a notion of tests, probabilistic event structures are related to another approach to probabilistic processes, viz. Markov decision processes. Tests and morphisms of event structures point the way to a more general theory in which, for example, event structures need not be confusion free. 1

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