X-Protege: An Ontology Editor for Defining Cartesian Types to Represent n-ary Relations

Arbitrary n-ary relations (n ≥ 1) can, in principle, be realized through binary relations obtained by a reification process which 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. In (Krieger and Willms, 2015), we have
laid the foundations for a theory-agnostic extension of RDFS and OWL and have implemented in the last year an extension of Prot´

ege´,

called ×-Prot´

ege´, which supports the definition of Cartesian types to represent n-ary relations and relation instances. Not only do we
keep the distinction between the domain and the range of an n-ary relation, but also introduce so-called extra arguments which can
be seen as position-oriented unnamed annotation properties and which are accessible to entailment rules. As the direct representation
of n-ary relations abolishes RDF triples, we have backed up ×-Prot´

ege´ by the semantic repository and entailment engine HFC which

supports tuples of arbitrary length. ×-Prot´

ege´ is programmed in Java and is made available under the Mozilla Public License.