 In some cases partitioning a reference class A can result in two sub-classes \((A \amp C)\) and \((A \amp \msim C)\) both homogeneous with respect to a given property B. This means that property B is held by all elements belonging to class \((A \amp C)\), but none of the elements belonging to \((A \amp \msim C)\). In all other cases the class A will be partitioned into k homogeneous sub-classes \((A \amp C_{k})\) such that