A kind of non-monotonic logical system invented by the logician Diderik Batens (1944– ). The style of proof is dynamic. Rules are of two kinds. The first are applied categorically. The second are applied provided that no abnormalities have been established. For example one might apply the disjunctive syllogism, $\left\{\neg \phi \vee \psi ,\phi \right\}⊢\psi$, provided that $\phi \wedge \neg \phi$ has not been proven. A record of the assumptions about abnormal formulae is kept, and if one is subsequently proved, the conclusion obtained by applying any rule it invalidates, and anything whose proof depends on this, is deleted. The proof system has a semantics where validity is defined in terms of truth preservation in those interpretations where abnormalities are minimized.