 Also, falsity (understood as receiving the value 0) and non-truth (understood as taking a value different from 1) fall apart in K3. As a result, contraposition fails in K3. Another example of a logic with a non-contraposable negation is Priest’s Logic of Paradox, LP, where negation is interpreted by \(f\osim \) and both \(i\) and 1 are designated values, see the entry on  paraconsistent logic.  If in K3 or in LP an implication \((A \supset B)\) is defined as material implication \((\osim A \vee B)\), then contraposition holds in the sense that \((A \supset B)\) entails \((\osim B \supset \osim A)\).