Abstract It is well known that any Boolean function in classical propositional calculus can be learned correctly if the training information system is good enough. In this paper, we extend that result for description logics. We prove that any concept in any description logic that extends $$mathcal {ALC}$$ ALC with some features amongst I (inverse roles), $$Q_k$$ Q k (qualified number restrictions with numbers bounded by a constant k ), and $$mathsf {Self}$$ Self (local reflexivity of a role) can be learned correctly if the training information system (specified as a finite interpretation) is good enough. That is, there exists a learning algorithm such that, for every concept C of those logics, there exists a training information system such that applying the learning algorithm to it results in a concept equivalent to? C . For this result, we introduce universal interpretations and bounded bisimulation in description logics and develop an appropriate learning algorithm. We also generalize common types of queries for description logics, introduce interpretation queries, and present some consequences.
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