Abduction is a method for finding the best explanation for observations. Arguably the most advanced approach to abduction, especially for natural language processing, is weighted abduction, which uses logical formulas with costs to guide inference. But it has no clear probabilistic semantics. In this paper we propose an approach that implements weighted abduction in Markov logic, which uses weighted first-order formulas to represent probabilistic knowledge, pointing toward a sound probabilistic semantics for weighted abduction. Application to a series of challenge problems shows the power and coverage of our approach.
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