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Safe deployment requires methods for characterizing what such systems can do, when they can do it, and what outcomes may result. We introduce Monte Carlo Query Synthesis (MCQS), an active query-synthesis method for learning symbolic stochastic capability models of BBAIs. MCQS models capabilities as conditional probability distributions over outcomes and formulates capability learning as an active learning problem over policies. Our approach uses Monte Carlo tree search to synthesize queries that induce BBAI execution trajectories with high discriminative value between extremal hypothesis models: the lattice meet and join corresponding to the most pessimistic and optimistic hypotheses consistent with the observations. 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