 We can now define that a sequent \(A \vdash B\) is valid in a compatibility model iff for every state \(w\) from that model, if \(A\) is true at \(w\), then so is \(B\); \(A \vdash B\) is called valid on a compatibility frame iff \(A \vdash B\) is valid in every model based on that frame. A rule is valid on a frame iff the validity of the premises sequents on that frame guarantees the validity of the conclusion sequent on the frame. The contraposition rule from the list (21) is valid on any compatibility frame. If the order-inversion expressed by contraposition is seen as a fundamental property of negation, a hierarchy of stronger negations can be obtained syntactically by postulating further principles and semantically by characterizing these principles by means of conditions on compatibility frames \((W, C, \leq)\), or relational frames \((W, C)\). This line of thought has led from a “kite” of negations in Dunn 1993 to “lopsided kites” of negations and an extended kite of negations in Shramko 2005, Dunn and Zhou 2005, see also Onishi 2015.