  This paper argues that a combined treatment of probabilities, time and
actions is essential for an appropriate logical account of the notion of
probability; and, based on this intuition, describes an expressive
probabilistic temporal logic for reasoning about actions with uncertain
outcomes. The logic is modal and higher-order: modalities annotated by actions
are used to express possibility and necessity of propositions in the next
states resulting from the actions, and a higher-order function is needed to
express the probability operator. The proposed logic is shown to be an adequate
extension of classical mathematical probability theory, and its expressiveness
is illustrated through the formalization of the Monty Hall problem.
