We present the learning algorithm underpinning ExactLearner, a tool for exactly learning and teaching EL terminologies. The algorithm is superpolynomial in the size of the concept expressions and vocabulary of the terminology, but not in the size of the whole terminology (which is optimal). We evaluate ExactLearner's performance on EL ontologies from the Oxford ontology repository and demonstrate that despite the algorithm being exponential, it successfully terminates for small and medium size

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... ntologies. We investigate the impact of various learner and teacher features and identify those most useful for learning.