Bayesian networks are directed acyclic graphs representing independence relationships among a set of random variables. A random variable can be regarded as a set of exhaustive and mutually exclusive propositions. We argue that there are several drawbacks resulting from the propositional nature and acyclic structure of Bayesian networks. To remedy these shortcomings, we propose a probabilistic network where nodes represent unary predicates and which may contain directed cycles. The proposed representation allows us to represent domain knowledge in a single static network even though we cannot determine the instantiations of the predicates before hand. The ability to deal with cycles also enables us to handle cyclic causal tendencies and to recognize recursive plans.

This paper presents a simple framework for Horn clause abduction, with probabilities associated with hypotheses. It is shown how this representation can represent any probabilistic knowledge representable in a Bayesian belief network. The main contributions are in finding a relationship between logical and probabilistic notions of evidential reasoning. This can be used as a basis for a new way to implement Bayesian Networks that allows for approximations to the value of the posterior probabilities, and also points to a way that Bayesian networks can be extended beyond a propositional language.

Poole, David L., Provan, Gregory M.

Within diagnostic reasoning there have been a number of proposed definitions of a diagnosis, and thus of the most likely diagnosis, including most probable posterior hypothesis, most probable interpretation, most probable covering hypothesis, etc. Most of these approaches assume that the most likely diagnosis must be computed, and that a definition of what should be computed can be made a priori, independent of what the diagnosis is used for. We argue that the diagnostic problem, as currently posed, is incomplete: it does not consider how the diagnosis is to be used, or the utility associated with the treatment of the abnormalities. In this paper we analyze several well-known definitions of diagnosis, showing that the different definitions of the most likely diagnosis have different qualitative meanings, even given the same input data. We argue that the most appropriate definition of (optimal) diagnosis needs to take into account the utility of outcomes and what the diagnosis is used for.

It has been well argued that correlation does not imply causation. Is the converse true: does non-correlation imply non-causation, or more plainly, does causation imply correlation? Here we argue that this is a useful intuition of the semantic essence of the faithfulness assumption of causal graphs. Although the statement is intuitively reasonable, it is not categorically true (but it is true with probability one), and this brings into question the validity of causal graphs. This work reviews Cartwright's arguments against faithfulness and presents a philosophical case in favor of the faithfulness assumption. This work also shows how the causal graph formalism can be used to troubleshoot scenarios where faithfulness is violated.

Henrion, Max, Druzdzel, Marek J.

Comprehensible explanations of probabilistic reasoning are a prerequisite for wider acceptance of Bayesian methods in expert systems and decision support systems. A study of human reasoning under uncertainty suggests two different strategies for explaining probabilistic reasoning: The first, qualitative belief propagation, traces the qualitative effect of evidence through a belief network from one variable to the next. This propagation algorithm is an alternative to the graph reduction algorithms of Wellman (1988) for inference in qualitative probabilistic networks. It is based on a qualitative analysis of intercausal reasoning, which is a generalization of Pearl's "explaining away", and an alternative to Wellman's definition of qualitative synergy. The other, Scenario-based reasoning, involves the generation of alternative causal "stories" accounting for the evidence. Comparing a few of the most probable scenarios provides an approximate way to explain the results of probabilistic reasoning. Both schemes employ causal as well as probabilistic knowledge. Probabilities may be presented as phrases and/or numbers. Users can control the style, abstraction and completeness of explanations.