Axiom:Preordering Axioms/Formulation 2

Definition
Let $\RR \subseteq S \times S$ be a relation on a set $S$.

$\RR$ is a preordering on $S$ $\RR$ satifies the axioms:

where:
 * $\circ$ denotes relation composition
 * $\Delta_S$ denotes the diagonal relation on $S$.

These criteria are called the preordering axioms.

Also see

 * Axiom:Preordering Axioms/Formulation 1 for an alternative formulation for the preordering axioms