  Abstraction is a commonly used process to represent some low-level system by
a more coarse specification with the goal to omit unnecessary details while
preserving important aspects. While recent work on abstraction in the situation
calculus has focused on non-probabilistic domains, we describe an approach to
abstraction of probabilistic and dynamic systems. Based on a variant of the
situation calculus with probabilistic belief, we define a notion of
bisimulation that allows to abstract a detailed probabilistic basic action
theory with noisy actuators and sensors by a possibly non-stochastic basic
action theory. By doing so, we obtain abstract Golog programs that omit
unnecessary details and which can be translated back to a detailed program for
actual execution. This simplifies the implementation of noisy robot programs,
opens up the possibility of using non-stochastic reasoning methods (e.g.,
planning) on probabilistic problems, and provides domain descriptions that are
more easily understandable and explainable.
