Exact Learning of TBoxes in EL and DL-Lite

We study polynomial time learning of description logic TBoxes in Angluin et al.’s framework of exact learning via queries. We admit entailment queries (“is a given subsumption entailed by the target TBox?”) and equivalence queries (“is a given TBox equivalent to the target TBox?”), assuming that the signature and logic of the target TBox are known. We present three main results: (1) TBoxes formulated in the extension of DL-Litecore with ELI-concepts on the right-hand side of concept inclusions can be learned in polynomial time. (2) Neither general nor acyclic EL TBoxes can be learned in polynomial time. (3) EL TBoxes with only concept names on the right-hand side of concept inclusions can be learned in polynomial time. It follows, in particular, that non-polynomial time learnability of EL TBoxes is caused by the interaction between existential restrictions on the right and left-hand side of concept inclusions.