 This replacement avoids a collapse into classical logic. Strong negation is called “strong” because it captures a notion of negation as definite falsity and because in the system N3 the strong negation of a formula entails its intuitionistic negation. The conjunction, disjunction, and strong negation fragment of N4 coincides with the logic of first-degree entailment FDE, also known as Dunn and Belnap’s useful four-valued logic (Belnap 1977a,b; Dunn 1976; Omori and Wansing 2017). Interestingly, contraposition as stated above holds for FDE, whereas it fails in FDE for multiple-premise sequents (see Problem 7, Section 8.10, p. 162 in Priest 2008).