n-ary relations (n ≥ 1) can in principle be realized through binary relations obtained by a reification process that introduces new individuals to which the additional arguments are linked via accessor properties. Modern ontologies which employ standards such as RDF and OWL have mostly obeyed this restriction, but have struggled with it nevertheless. Additional arguments for representing, e.g., valid time, grading, uncertainty, negation, trust, sentiment, or additional verb roles (for ditransitive verbs and adjuncts) are often better modeled in relation and information extraction systems as direct arguments of the relation instance, instead of being hidden in deep structures. In order to address non-binary relations directly, ontologies must be extended by Cartesian types, ultimately leading to an extension of the standard entailment rules for RDFS and OWL. In order to support ontology construction, ontology editors such as Prot´ ege´ have to be adapted as well.