Learning Query Inseparable εℒℋ Ontologies

Abstract

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.

On the Complexity of Learning Description Logic Ontologies

“…Recently, it has been shown that if the ABox is fixed and one only aims at preserving IQ results w.r.t. the fixed ABox (not logical equivalence between the hypothesis and the target) then there is a polynomial time algorithm for ELH terminologies [37]. We denote this learning framework by F(ELH, A, IQ) where A is the fixed ABox.…”

“…He constructed an artificial counterexample to prove the result and the argument relies on cryptographic assumptions. Another (artificial) counterexample appears in the work by Ozaki et al (2020) [37]. The argument in this case does not rely on cryptographic assumptions.…”

Separability and Its Approximations in Ontology-based Data Management

“…The Active Learning task initially introduced by [2] has been studied as a possible framework for learning queries from examples in relational databases [64] and in the presence of DL-Lite ontologies [30]. Moreover, instances of the framework in [2] can be found in [42] and in [57]. In particular, the goal of [42] is to learn an ontology that is equivalent to a target ontology, while the goal of [57] is to learn an ontology that is query inseparable with respect to a target ontology T and a query language Q, i.e.…”

“…Moreover, instances of the framework in [2] can be found in [42] and in [57]. In particular, the goal of [42] is to learn an ontology that is equivalent to a target ontology, while the goal of [57] is to learn an ontology that is query inseparable with respect to a target ontology T and a query language Q, i.e. given a set of ground atoms (ABox) A, the learned ontology H must be such that H, A |= q if and only if T , A |= q, for every q ∈ Q.…”

Learning Description Logic Ontologies: Five Approaches. Where Do They Stand?

“…It has been shown that the EL fragments EL lhs and EL rhs -the EL fragments that allow only conjunctions of concept names on the right-side and on the left-side of CIs, respectively-are polynomial time exactly learnable from entailments [23,24,38,37] 4 , however, this is not the case for EL. The learning framework is the one in Example 1 and the problem statement is the same as in the original approach.…”