This is an important paper, that has frequently been cited after a first version of it was pre-printed in 1990. The author carefully develops a semantic theory of persistent default rules, that correctly deals with benchmark examples from the literature. Three natural notions of dynamic entailment are presented and one is chosen for the formal representation of default reasoning. Notably, conclusions drawn from sequences of premises containing default assumptions have the shape “presumably \(A\)”, indicating in the object-language the defeasibility of \(A\). The author also points out two anomalies of defaults in update semantics, namely ‘Strengthening with a consequent’ and ‘Disjunction of antecedents’ fail to be valid.