Believing Change and Changing Belief

We present a rst order logic of time chance and probability that is capable of expressing the relation between subjective probability and objective chance at di erent times Us ing this capability we show how the logic can distinguish between causal and evidential correlation by distinguishing between condi tions events and actions that in uence the agent s belief in chance and the agent believes to in uence chance Furthermore the semantics of the logic captures common sense inferences concerning objective chance and causality We show that an agent s sub jective probability is the expected value of its beliefs concerning objective chance We also prove that an agent using this represen tation believes with certainty that the past cannot be causally in uenced