Generating Bayesian Networks from Probability Logic Knowledge Bases
This work addresses the challenge of automating probabilistic reasoning for AI systems, but it is incremental as it builds on existing logic and network frameworks.
The authors tackled the problem of generating Bayesian networks from first-order probability logic knowledge bases, presenting a method that ensures all necessary probabilistic information is included and proving the correctness of their algorithm for computing conditional probabilities.
We present a method for dynamically generating Bayesian networks from knowledge bases consisting of first-order probability logic sentences. We present a subset of probability logic sufficient for representing the class of Bayesian networks with discrete-valued nodes. We impose constraints on the form of the sentences that guarantee that the knowledge base contains all the probabilistic information necessary to generate a network. We define the concept of d-separation for knowledge bases and prove that a knowledge base with independence conditions defined by d-separation is a complete specification of a probability distribution. We present a network generation algorithm that, given an inference problem in the form of a query Q and a set of evidence E, generates a network to compute P(Q|E). We prove the algorithm to be correct.