  We exploit qualitative probabilistic relationships among variables for
computing bounds of conditional probability distributions of interest in
Bayesian networks. Using the signs of qualitative relationships, we can
implement abstraction operations that are guaranteed to bound the distributions
of interest in the desired direction. By evaluating incrementally improved
approximate networks, our algorithm obtains monotonically tightening bounds
that converge to exact distributions. For supermodular utility functions, the
tightening bounds monotonically reduce the set of admissible decision
alternatives as well.
