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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.
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