  Bayesian knowledge bases (BKBs) are a generalization of Bayes networks and
weighted proof graphs (WAODAGs), that allow cycles in the causal graph.
Reasoning in BKBs requires finding the most probable inferences consistent with
the evidence. The cost-sharing heuristic for finding least-cost explanations in
WAODAGs was presented and shown to be effective by Charniak and Husain.
However, the cycles in BKBs would make the definition of cost-sharing cyclic as
well, if applied directly to BKBs. By treating the defining equations of
cost-sharing as a system of equations, one can properly define an admissible
cost-sharing heuristic for BKBs. Empirical evaluation shows that cost-sharing
improves performance significantly when applied to BKBs.
