 Whilst satisfying the contraposition rule \(A \vdash B \slashrel \osim B \vdash \osim A\) is a basic property of negation as a normal impossibility operator, there exist unary connectives that are referred to as negations, although they do not satisfy contraposition. Prominent examples of logics with a non-contraposable negation in addition to the already mentioned logics K3, Ł\(_3\), and LP, are Nelson’s logics N3, N4, and N4\(^{\bot}\) of constructive logic with so-called strong negation (see Nelson 1949; Gurevich 1977; Almukdad and Nelson 1984; Wansing 1993, 2001; Dunn 2000; Odintsov 2008). These logics contain intuitionistic implication as a primitive connective. Nelson (1959), however, also considers a variant of N3 with a contraposable strong negation. In this system S, the contraction axiom