On the Power and Limitations of Examples for Description Logic Concepts (Extended 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 characterizations, 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 characterizations are relevant for debugging purposes, and their existence is a necessary condition for exact learnability with membership queries.