Generalized Domain-Range Restrictions

Proposing a certain notion of logical completeness as a novel quality criterion for ontologies, we identify and characterise a class of logical propositions which naturally extend domain and range restrictions commonly known from diverse ontology modelling approaches. We argue for the intuitivity of this kind of axioms and show that they fit equally well into formalisms based on rules as well as ones based on description logics. Extending the attribute exploration technique from formal concept analysis (FCA), we present an algorithm for the efficient interactive specification of all axioms of this form valid in a domain of interest. We compile some results that apply when role hierarchies and symmetric roles come into play and demonstrate the presented method in a small example.