Exact Learning Description Logic Ontologies from Data Retrieval Examples.

We investigate the complexity of learning description logic ontologies in Angluin et al.'s framework of exact learning via queries posed to an oracle. We consider membership queries of the form is individual a a certain answer to a data retrieval query q in a given ABox and the unkown target TBox? and equivalence queries of the form is a given TBox equivalent to the unknown target TBox?.We show that (i) DL-Lite TBoxes with role inclusions and ELI concept expressions on the right-hand side of inclusions and (ii) EL TBoxes without complex concept expressions on the right-hand side of inclusions can be learned in polynomial time. Both results are proved by a non-trivial reduction to learning from subsumption examples.We also show that arbitrary EL TBoxes cannot be learned in polynomial time.