\begin{definition}[Definition:Negatively Transitive Relation]
Let $\RR$ be a relation on a set $S$.
Then $\RR$ is '''negatively transitive''' {{iff}}:
:$\forall x, y, z \in S: \neg \paren {x \mathrel \RR y} \land \neg \paren {y \mathrel \RR z} \implies \neg \paren {x \mathrel \RR z}$
By De Morgan's Laws, this can be given the alternative form:
:$\forall x, y, z \in S: \paren {x \mathrel \RR z} \implies \paren {x \mathrel \RR y} \lor \paren {y \mathrel \RR z}$
\end{definition}