Definition:Strict Weak Ordering

Definition
A strict weak ordering on a set $S$ is a relation $\mathcal R$ such that:


 * $(1): \quad \mathcal R$ is a strict partial ordering


 * $(2): \quad$ The incomparability relation $\mathcal R'$ defined as:


 * $a \mathrel {\mathcal R'} b := \neg \left({a \mathrel {\mathcal R} b}\right) \land \neg \left({b \mathrel {\mathcal R} a}\right)$


 * is transitive.