This article presents a theory of how individuals reason from inconsistency to consistency. The theory is based on 3 main principles. First, individuals try to construct a single mental model of a possibility that satisfies a current set of propositions, and if the task is impossible, they infer that the set is inconsistent. Second, when an inconsistency arises from an incontrovertible fact, they retract any singularly dubious proposition or any proposition that is inconsistent with the fact; otherwise, they retract whichever proposition mismatches the fact. A mismatch can arise from a proposition that has only mental models that conflict with the fact or fail to represent it. Third, individuals use their causal knowledge-in the form of models of possibilities-to create explanations of what led to the inconsistency. A computer program implements the theory, and experimental results support each of its principles.