Learnability Results for Elementary Formal Systems 12+

📙 Elementary formal systems are a kind of logicprograms. We give a comprehensive relationship modelfor a broad range of classes of elementary formalsystems (EFS) and Prolog Programs along with theirlearnability results in the frameworks of learningin the limit, learning from queries, learning fromentailment, and statistical framework of probablyapproximately correct (PAC) learning. Therelationship model accompanies the proofs ofcontainment, partial containment, and/orincompatibilities present among these classes.Further, we study exact learning of two classes ofProlog programs (or equivalently elementary formalsystems) from entailment. These two classes,hereditary and reductive, of Prolog programs withoutlocal variables contain many useful programs such asadd, append, lenght, merge, split, delete, member,prefix, and suffix. We present an algorithm toexactly learn hereditary and reductiveProlog programs and analyze it for its correctness.Moreover, the algorithm learns hereditary Prologprograms in polynomial time.