this paper, Rumelhart presented compelling evidence that text comprehension must be a distributed process that combines both top-down and bottom-up inferences. Strangely, this dual mode of inference, so characteristic of Bayesian analysis, did not match the capabilities of either the "certainty factors" calculus or the inference networks of PROSPECTOR -- the two major contenders for uncertainty management in the 1970s. I thus began to explore the possibility of achieving distributed computation in a "pure" Bayesian framework, so as not to compromise its basic capacity to combine bi-directional inferences (i.e., predictive and abductive) . Not caring much about generality at that point, I picked the simplest structure I could think of (i.e., a tree) and tried to see if anything useful can be computed by assigning each variable a simple processor, forced to communicate only with its neighbors. This gave rise to the tree-propagation algorithm reported in [15] and, a year later, the Kim-Pearl algorithm [12], which supported not only bi-directional inferences but also intercausal interactions, such as "explaining-away." These two algorithms were described in Section 2 of Fusion.

This paper presents a logical formalism for representing and reasoning with statistical knowledge. One of the key features of the formalism is its ability to deal with qualitative statistical information. It is argued that statistical knowledge, especially that of a qualitative nature, is an important component of our world knowledge and that such knowledge is used in many different reasoning tasks. The work is further motivated by the observation that previous formalisms for representing probabilistic information are inadequate for representing statistical knowledge. The representation mechanism takes the form of a logic that is capable of representing a wide variety of statistical knowledge, and that possesses an intuitive formal semantics based on the simple notions of sets of objects and probabilities defined over those sets. Furthermore, a proof theory is developed and is shown to be sound and complete. The formalism offers a perspicuous and powerful representational tool for stat...

Abstract not found

This extended abstract presents a logic, called Lp, that is capable of representing and reasoning with a wide variety of both qualitative and quantitative statistical information. The advantage of this logical formalism is that it offers a declarative representation of statistical knowledge; knowledge represented in this manner can be used for a variety of

It is well known that, in directed Markov fields, the pairwise Markov condition does not imply the global Markov condition, unless the distribution is strictly positive. We introduce a stronger version of the pairwise condition which requires that every nonadjacent pair be independent conditional on every set that separates the pair in the graph. We show that this stronger condition is equivalent to the global Markov condition (for all probability distributions.) We generalize this result to abstract dependency models, and show that a weaker condition holds for compositional graphoids. 1