Randomness and independence in nonmonotonic reasoning

If randomness is at the heart of Kyburg's (1971) theory of epistemological probability, independence (especially conditional independence) is at the heart of the work of Pearl (1988), Lauritzen and Speigelhalter (1988) and Shachter (1986) on causal probabilistic nets. Both ideas extend the range of inferences that can be made from a set of probabilities (or statistical statements), but in very different ways.