Actively Learning Concepts and Conjunctive Queries under ELr-Ontologies

TL;DR

This paper investigates the active learning of concepts and conjunctive queries within ELr-ontologies, demonstrating polynomial learnability for certain classes and limitations for others, advancing understanding of ontology-based query learning.

Contribution

It introduces polynomial-time active learning algorithms for specific classes of concepts and queries in ELr-ontologies, and identifies limitations with ELI-ontologies.

Findings

EL-concepts, symmetry-free ELI-concepts, and certain CQs are learnable in polynomial time.

Active learning uses membership and equivalence queries based on ABoxes.

EL-concepts are not polynomially learnable with ELI-ontologies.

Abstract

We consider the problem to learn a concept or a query in the presence of an ontology formulated in the description logic ELr, in Angluin's framework of active learning that allows the learning algorithm to interactively query an oracle (such as a domain expert). We show that the following can be learned in polynomial time: (1) EL-concepts, (2) symmetry-free ELI-concepts, and (3) conjunctive queries (CQs) that are chordal, symmetry-free, and of bounded arity. In all cases, the learner can pose to the oracle membership queries based on ABoxes and equivalence queries that ask whether a given concept/query from the considered class is equivalent to the target. The restriction to bounded arity in (3) can be removed when we admit unrestricted CQs in equivalence queries. We also show that EL-concepts are not polynomial query learnable in the presence of ELI-ontologies.