Automated acquisition (learning) of ontologies from data has attracted research interest because it can complement manual, expensive construction of ontologies. We investigate the problem of General Terminology Induction in OWL, i.e. acquiring general, expressive TBox axioms (hypotheses) from an ABox (data). We define novel measures designed to rigorously evaluate the quality of hypotheses while respecting the standard semantics of OWL. We propose an informed, data-driven algorithm that constructs class expressions for hypotheses in OWL and guarantees completeness. We empirically evaluate the quality measures on two corpora of ontologies and run a case study with a domain expert to gain insight into applicability of the measures and acquired hypotheses. The results show that the measures capture different quality aspects and not only correct hypotheses can be interesting.