Strong Separation of Learning Classes

Suppose LC1 and LC2 are two machine learning classes each based on a criterion of success. Suppose, for every machine which learns a class of functions according to the LC1 criterion of success, there is a machine which learns this class according to the LC2 criterion. In the case where the converse does not hold LC1 is said to be separated from LC2. It is shown that for many such separated learning classes from the literature a much stronger separation holds: (∀C ∈ LC1)(∃C ′ ∈ (LC2−LC1))[C ′ ⊃ C]. It is also shown that there is a pair of separated learning classes from the literature for which the stronger separation just above does not hold. A philosophical heuristic toward the design of artificially intelligent learning programs is presented with each strong separation result.