Axiom:Preordering Axioms/Formulation 1

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

$\RR$ satisfies the preordering axioms on $S$ $\RR$ satifies the axioms:

Also see

 * Axiom:Preordering Axioms/Formulation 2 for an alternative formulation for the preordering axioms