  This paper provides a formal and practical framework for sound abstraction of
probabilistic actions. We start by precisely defining the concept of sound
abstraction within the context of finite-horizon planning (where each plan is a
finite sequence of actions). Next we show that such abstraction cannot be
performed within the traditional probabilistic action representation, which
models a world with a single probability distribution over the state space. We
then present the constraint mass assignment representation, which models the
world with a set of probability distributions and is a generalization of mass
assignment representations. Within this framework, we present sound abstraction
procedures for three types of action abstraction. We end the paper with
discussions and related work on sound and approximate abstraction. We give
pointers to papers in which we discuss other sound abstraction-related issues,
including applications, estimating loss due to abstraction, and automatically
generating abstraction hierarchies.

Artificial Intelligence