  Investigating whether pre-trained language models (LMs) can function as
knowledge bases (KBs) has raised wide research interests recently. However,
existing works focus on simple, triple-based, relational KBs, but omit more
sophisticated, logic-based, conceptualised KBs such as OWL ontologies. To
investigate an LM's knowledge of ontologies, we propose OntoLAMA, a set of
inference-based probing tasks and datasets from ontology subsumption axioms
involving both atomic and complex concepts. We conduct extensive experiments on
ontologies of different domains and scales, and our results demonstrate that
LMs encode relatively less background knowledge of Subsumption Inference (SI)
than traditional Natural Language Inference (NLI) but can improve on SI
significantly when a small number of samples are given. We will open-source our
code and datasets.
