  Agents interacting with an incompletely known world need to be able to reason
about the effects of their actions, and to gain further information about that
world they need to use sensors of some sort. Unfortunately, both the effects of
actions and the information returned from sensors are subject to error. To cope
with such uncertainties, the agent can maintain probabilistic beliefs about the
state of the world. With probabilistic beliefs the agent will be able to
quantify the likelihood of the various outcomes of its actions and is better
able to utilize the information gathered from its error-prone actions and
sensors. In this paper, we present a model in which we can reason about an
agent's probabilistic degrees of belief and the manner in which these beliefs
change as various actions are executed. We build on a general logical theory of
action developed by Reiter and others, formalized in the situation calculus. We
propose a simple axiomatization that captures an agent's state of belief and
the manner in which these beliefs change when actions are executed. Our model
displays a number of intuitively reasonable properties.
