Eyal Shlomo Shimony

New knowledge is incrementally introduced to an existing knowledge base in a typical knowledge-engineering cycle. Unfortunately, at most given stages, the knowledge base is incomplete but must still satisfy sufficient consistency conditions in order to provide sound semantics. Maintaining semantics for uncertainty is of primary concern. We examine Bayesian knowledge bases (BKBs), which are a generalization of Bayesian networks. BKBs provide a highly flexible and intuitive representation following a basic "if-then" structure in conjunction with probability theory. We present new theoretical and algorithmic results concerning BKBs and how they can naturally and implicitly preserve semantics as new knowledge is added. In particular, equivalence of rule weights and conditional probabilities is achieved through stability of inferencing in BKBs. Furthermore, efficient algorithms are developed to guarantee stability of BKBs during construction. Finally, we examine and prove formal conditions that hold during the incremental construction of BKBs.