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Cost-based abduction (CBA) is an important AI formalism for representing knowledge under uncertainty. In this formalism, evidence to be explained is treated as a goal to be proven, proofs have costs based on how much needs to be assumed to complete the proof, and the set of assumptions needed to complete the least-cost proof are taken as the best explanation for the given evidence. The problem of finding the least-cost proof for a given CBA system is NP-hard and current techniques have exponential complexity in the worst case. Computational intelligence approaches to this problem have not been previously explored. In this paper, we show how high order recurrent networks can be used to find least-cost proofs for CBA instances. We describe experimental results on 80 CBA instances using networks of up to 68 neurons.