There are several categorizations of binary relations based on which 
axioms they hold.  These are called orders.
 * preorder
 * weak order
 * strict weak order
 * strict order
 * strict partial order
 * equivalence

From the orderings a framework is built up. 
 * strict order
 * weak order

Examples: 
 * subset on all sets is a preorder
 * => on R is a strict order
 * "=>" on R^2 is a antisymmetric preorder
 * ||  || (magnitude) on R^2 is a weak order