Probabilistic Semantics for Cost Based Abduction

Cost-based abduction attempts to find the best explanation for a set of facts by finding a minimal cost proof for the facts. The costs are computed by summing the costs of the assumptions necessary for the proof plus the cost of the rules. We examine existing methods for constructing explanations (proofs), as a minimization problem on a DAG. We then define a probabilistic semantics for the costs, and prove the equivalence of the cost minimization problem to the Bayesian network MAP solution of the system.