We present a method for dynamically gen erating Bayesian networks from knowledge bases consisting of first-order probability logic sentences. We present a subset of proba bility 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 knowl edge base contains all the probabilistic infor mation necessary to generate a network. We define the concept of d-separation for knowl edge 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 net work generation algorithm that, given an in ference problem in the form of a query Q and a set of evidence E, generates a network to compute P(QIE). We prove the algorithm to be correct. proaches that provides a network generation algorithm presents a complete semantics for the knowledge base representation language, independent of that particu lar generation algorithm. Such a semantics is impor tant for two reasons. First, since a user of a network generation system encodes information in the knowl edge representation language, he must know the pre cise meanin � s of sentences in that language. As Well man, et.al. l1992] point out, this semantics should be specified without recourse to the details of the network generation process. Second, one would like to be able to prove that the network generation algorithm is cor rect. In order to be correct, the algorithm must faith fully map probabilistic relations in the knowledge base into probabilistic relations in the network. In order to be able to prove this, we must have a formal specifi cation of the probabilistic relations in the knowledge base. We address the problem of providing a formal seman tics for the knowledge base by using first-order proba bility logic as the representation language. We present a subset of probability logic sufficient for represent ing the class of Bayesian networks with discrete-valued nodes. We impose constraints on the form of the sen tences that guarantee that the knowledge base con tains all the probabilistic information necessary to gen erate a network. We define an independence seman tics for the knowledge base that is analogous to Pearl's [1988] definition of d-separation for Bayesian networks. We prove that a knowledge base with independence conditions defined by d-separation is a complete spec-
Generating a Bayesian Network from a probabilistic knowledge-base was pioneered by Peter Haddawy REF .
Generating Bayesian Networks from Probability Logic Knowledge Bases
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