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Probabilistic Logic For Belief Nets, K. Andersen, John Hooker
Probabilistic Logic For Belief Nets, K. Andersen, John Hooker
John Hooker
We describe how to combine probabilistic logic and Bayesian networks to obtain a new frame-work ("Bayesian logic") for dealing with uncertainty and causal relationships in an expert system. Probabilistic logic, invented by Boole, is a technique for drawing inferences from uncertain propositions for which there are no independence assumptions. A Bayesian network is a "belief net" that can represent complex conditional independence assumptions. We show how to solve inference problems in Bayesian logic by applying Benders decomposition to a nonlinear programming formulation. We also show that the number of constraints grows only linearly with the problem size for a large …