A probability threshold belief set is deductively closed exactly when the distribution has a step, and the new revision rule is the minimal Kullback-Leibler change that raises the new statement to the threshold.
The British Journal for the Philosophy of Science69(2), 509–552 (2016)
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On Lockean beliefs that are deductively closed and minimal change
A probability threshold belief set is deductively closed exactly when the distribution has a step, and the new revision rule is the minimal Kullback-Leibler change that raises the new statement to the threshold.