Definition:Strict Weak Ordering

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


 * $\mathcal R$ is a strict partial ordering


 * The incomparability relation $\mathcal R'$ defined as:


 * $a \mathcal R' b := \neg a \mathcal R b \land \neg b \mathcal R a$

is transitive.