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Algorithmic Learning Theory analogical reasoning Angluin applied Artificial Intelligence atoms bound called clause complexity computation concept class consistent constraint construct corresponding defined Definition denote domain elements equal matrix error exists Figure finite set framework given grammar higher-order higher-order unification hypothesis space identifies inductive inference inferable from positive inference patterns input integer k-EML knowledge learner learning algorithm learning procedure Lemma linear set logic program loss function Machine Learning macro-rule mapping matrix grammar matrix rule method minimal n-tuples negative examples neural nodes number of examples objects Occam algorithm operator output PAC-learning paper parameter paraphrasing pattern languages polynomial polynomial learnability polynomial-time positive data positive examples predicate probability distribution Proof pseudo-terms queries recursive functions regular languages representation class represented respect result rlgg sample self-organizing semilinear set strings structure subset substitution target concept term rewriting system Theorem unification variables vector