A logical alarm for misaligned binary classifiers

If two agents disagree in their decisions, we may suspect they are not both correct. This intuition is formalized for evaluating agents that have carried out a binary classification task. Their agreements and disagreements on a joint test allow us to establish the only group evaluations logically consistent with their responses. This is done by establishing a set of axioms (algebraic relations) that must be universally obeyed by all evaluations of binary responders. A complete set of such axioms are possible for each ensemble of size N. The axioms for $N = 1, 2$ are used to construct a fully logical alarm - one that can prove that at least one ensemble member is malfunctioning using only unlabeled data. The similarities of this approach to formal software verification and its utility for recent agendas of safe guaranteed AI are discussed.