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# ternary relation (TernaryRelation)

TernaryRelations relate three items. The two subclasses of TernaryRelation are TernaryPredicate and BinaryFunction.

## Ontology

SUMO / BASE-ONTOLOGY

## Class(es)

 class

inheritable relation

ternary relation

## Superclass(es)

 entity

abstract

relation

ternary relation

## Subclass(es)

binary function  ternary predicate

## Coordinate term(s)

binary function  binary predicate  binary relation  case role  function  intentional relation  list  object attitude  partial valued relation  predicate  probability relation  propositional attitude  quaternary function  quaternary predicate  quaternary relation  quintary predicate  quintary relation  relation extended to quantities  single valued relation  spatial relation  temporal relation  ternary function  ternary predicate  total valued relation  unary function  variable arity relation

## Axioms (3)

relation is disjointly decomposed into binary relation,ternary relation,quaternary relation,quintary relation,variable arity relation.
`(disjointDecomposition Relation BinaryRelation TernaryRelation QuaternaryRelation QuintaryRelation VariableArityRelation)`

If rel is an instance of ternary relation, then there don't exist item1,item2,item3,item4, so that rel(item1,item2,item3,item4,) holds.
```(=>
(instance ?REL TernaryRelation)
(not
(exists
(?ITEM1 ?ITEM2 ?ITEM3 ?ITEM4 @ROW)
(holds ?REL ?ITEM1 ?ITEM2 ?ITEM3 ?ITEM4 @ROW))))```

```(=>
(and
(instance ?REL RelationExtendedToQuantities)
(instance ?REL TernaryRelation)
(instance ?NUMBER1 RealNumber)
(instance ?NUMBER2 RealNumber)
(holds ?REL ?NUMBER1 ?NUMBER2 ?VALUE))
(forall
(?UNIT)
(=>
(instance ?UNIT UnitOfMeasure)
(holds
?REL
(MeasureFn ?NUMBER1 ?UNIT)
(MeasureFn ?NUMBER2 ?UNIT)
(MeasureFn ?VALUE ?UNIT)))))```