We investigate the complexity of learning query inseparable εℒℋ 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.

In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set of concept inclusions instead of implications. In this setting, concept expressions can be arbitrarily large. Thus, it is not clear whether a finite base exists and, if so, how large concept expressions may need to be. We first revisit results in the literature for mining EL bases from finite interpretations. Those mainly focus on finding a finite base or on fixing the role depth but potentially losing some of the valid concept inclusions with higher role depth. We then present a new strategy for mining EL bases which is adaptable in the sense that it can bound the role depth of concepts depending on the local structure of the interpretation. Our strategy guarantees to capture all EL concept inclusions holding in the interpretation, not only the ones up to a fixed role depth.

In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set of concept inclusions instead of implications. In this setting, concept expressions can be arbitrarily large. Thus, it is not clear whether a finite base exists and, if so, how large concept expressions may need to be. We first revisit results in the literature for mining EL ⊥ bases from finite interpretations. Those mainly focus on finding a finite base or on fixing the role depth but potentially losing some of the valid concept inclusions with higher role depth. We then present a new strategy for mining EL ⊥ bases which is adaptable in the sense that it can bound the role depth of concepts depending on the local structure of the interpretation. Our strategy guarantees to capture all EL ⊥ concept inclusions holding in the interpretation, not only the ones up to a fixed role depth.

We investigate learnability of possibilistic theories from entailments in light of Angluin's exact learning model. We consider cases in which only membership, only equivalence, and both kinds of queries can be posed by the learner. We then show that, for a large class of problems, polynomial time learnability results for classical logic can be transferred to the respective possibilistic extension. In particular, it follows from our results that the possibilistic extension of propositional Horn theories is exactly learnable in polynomial time. As polynomial time learnability in the exact model is transferable to the classical probably approximately correct model extended with membership queries, our work also establishes such results in this model.