An n-ary relation is a relation that maps between a subject and two or more values. This is distinct from the most common type of relation, a binary relation, which maps between a single subject and a single value. An n-ary relation cannot be split up into n binary relations, because the relations it defines are all interconnected in some way.
 Theoretical basis
The W3C's paper on the subject, "Defining N-ary Relations on the Semantic Web", lists four types of n-ary relations:
- Additional attributes describing a relation - an example is "Christine has breast tumor with high probability". In this case, there is one main relation, and one or more additional relations that modify the main one.
- Different aspects of the same relation - an example is "Steve has temperature, which is high, but falling". In this case, all relations are equal in importance, and all describe the subject in some way.
- N-ary relation with no distinguished participant - an example is "John buys a 'Lenny the Lion' book from books.example.com for $15 as a birthday gift". In this case, all relations are equal in importance, and they do not describe the subject; they describe some other entity (in this case, a purchase).
- Using lists for arguments in a relation - an example is "United Airlines flight 3177 visits the following airports: LAX, DFW, and JFK". In this case, the order of the relations matters as well.
The RDF/OWL approach to n-ary relations is to map them using binary relations, by creating an intermediate entity that serves as the subject for the entire set of relations; this entity is then in turn made the object for a relation in which the main subject is the subject. Since this intermediate entity does not have a real-world name of its own, it is usually given the name of the class to which it belongs, followed by an index number. Here for instance, is a portion of the RDF definition  for the second example above:
<Temperature_Observation rdf:nodeID="Temperature_Observation_1"> <temperature_trend rdf:datatype="http://www.w3.org/2001/XMLSchema#string">Falling</temperature_trend> <temperature_value rdf:datatype="http://www.w3.org/2001/XMLSchema#string">Elevated</temperature_value> </Temperature_Observation> <Person rdf:ID="Steve"> <has_temperature rdf:resource="#Temperature_Observation_1"/> </Person>
This could get represented within a semantic Wiki in a similar way. Here is one approach to representing it, in an article named "Steve":
[[subClassOf::Person]] [[has temperature:: [[Temperature Observation:: [[temperature trend:=Falling]] [[temperature value:=Elevated]] ]] ]]
Here is another semantic wiki approach, incorporating free text:
Steve is a [[subClassOf::Person]]. [[[has temperature:: Steve's temperature is [[has trend:=Falling]], but still [[has value:=Elevated]]. ]]]
As before, the data types would be represented in the articles for those attributes.
 Semantic wiki support
Please list here any semantic wikis that support n-ary relations:
- Semantic MediaWiki 1.0 supports compound, or many-valued, properties, that resemble n-ary relations, though with some limitations; see Many-valued properties.
- BOWiki supports n-ary relations and reasoning