On the Power and Limitations of Examples for Description Logic Concepts

TL;DR

This paper explores how effectively labeled examples can describe description logic concepts, analyzing the existence and computational aspects of finite characterizations across various logics and ontologies.

Contribution

It systematically studies the existence and computability of finite characterizations for description logic concepts, bridging theory and practical applications.

Findings

Finite characterizations exist for certain description logics.

Computability of finite characterizations varies across logics.

Results inform concept learning and debugging in DLs.

Abstract

Labeled examples (i.e., positive and negative examples) are an attractive medium for communicating complex concepts. They are useful for deriving concept expressions (such as in concept learning, interactive concept specification, and concept refinement) as well as for illustrating concept expressions to a user or domain expert. We investigate the power of labeled examples for describing description-logic concepts. Specifically, we systematically study the existence and efficient computability of finite characterisations, i.e. finite sets of labeled examples that uniquely characterize a single concept, for a wide variety of description logics between EL and ALCQI, both without an ontology and in the presence of a DL-Lite ontology. Finite characterisations are relevant for debugging purposes, and their existence is a necessary condition for exact learnability with membership queries.