Dekang Lin

Dekang Lin, Randy Goebel

We propose an abductive diagnosis theory that integrates probabilistic, causal and taxonomic knowledge. Probabilistic knowledge allows us to select the most likely explanation; causal knowledge allows us to make reasonable independence assumptions; taxonomic knowledge allows causation to be modeled at different levels of detail, and allows observations be described in different levels of precision. Unlike most other approaches where a causal explanation is a hypothesis that one or more causative events occurred, we define an explanation of a set of observations to be an occurrence of a chain of causation events. These causation events constitute a scenario where all the observations are true. We show that the probabilities of the scenarios can be computed from the conditional probabilities of the causation events. Abductive reasoning is inherently complex even if only modest expressive power is allowed. However, our abduction algorithm is exponential only in the number of observations to be explained, and is polynomial in the size of the knowledge base. This contrasts with many other abduction procedures that are exponential in the size of the knowledge base.

Dekang Lin

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.