Separable and transitive graphoids
  We examine three probabilistic formulations of the sentence a and b are
totally unrelated with respect to a given set of variables U. First, two
variables a and b are totally independent if they are independent given any
value of any subset of the variables in U. Second, two variables are totally
uncoupled if U can be partitioned into two marginally independent sets
containing a and b respectively. Third, two variables are totally disconnected
if the corresponding nodes are disconnected in every belief network
representation. We explore the relationship between these three formulations of
unrelatedness and explain their relevance to the process of acquiring
probabilistic knowledge from human experts.
