Several methodologies have been proposed, including certainty factors, fuzzy sets, Dempster-Shafer theory, and probability theory. The independence that is encoded in a Bayesian network is that each variable is independent of its non-descendents given its parents.
Bayesian networks aid in knowledge acquisition by specifying which probabilities are needed.
Where the network structure is sparse, the number of probabilities required can be much less than the number required if there were no independencies. The definition of a Bayesian network does not constrain how a variable depends on its parents. Often, however, there is much structure in these probability functions that can be exploited for knowledge acquisition and inference. Another is where the the function can be described using a binary operator that can be applied to values from each of the parent variables. Causal independence refers to the situation where multiple causes contribute independently to a common effect.