Learning Query Inseparable εℒℋ Ontologies

Abstract

We investigate the complexity of learning query inseparable eℒℋ ontologies in a variant of Angluin's exact learning model. Given a fixed data instance A* and a query language 𝒬, we are interested in computing an ontology ℋ that entails the same queries as a target ontology 𝒯 on A*, that is, ℋ and 𝒯 are inseparable w.r.t. A* and 𝒬. The learner is allowed to pose two kinds of questions. The first is ‘Does (𝒯,A)⊨ q?’, with A an arbitrary data instance and q and query in 𝒬. An oracle replies this question with ‘yes’ or ‘no’. In the second, the learner asks ‘Are ℋ and 𝒯 inseparable w.r.t. A* and 𝒬?’. If so, the learning process finishes, otherwise, the learner receives (A*,q) with q ∈ 𝒬, (𝒯,A*) |= q and (ℋ,A*) ⊭ q (or vice-versa). Then, we analyse conditions in which query inseparability is preserved if A* changes. Finally, we consider the PAC learning model and a setting where the algorithms learn from a batch of classified data, limiting interactions with the oracles.