Elementary formal systems are a kind of logic programs. We give a comprehensive relationship model for a broad range of classes of elementary formal systems (EFS) and Prolog Programs along with their learnability results in the frameworks of learning in the limit, learning from queries, learning from entailment, and statistical framework of probably approximately correct (PAC) learning. The relationship model accompanies the proofs of containment, partial containment, and/or incompatibilities present among these classes. Further, we study exact learning of two classes of Prolog programs (or equivalently elementary formal systems) from entailment. These two classes, hereditary and reductive, of Prolog programs without local variables contain many useful programs such as add, append, lenght, merge, split, delete, member, prefix, and suffix. We present an algorithm to exactly learn hereditary and reductive Prolog programs and analyze it for its correctness. Moreover, the algorithm learns hereditary Prolog programs in polynomial time.
