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))))

if rel is an instance of relation extended to quantities and rel is an instance of ternary relation and number1 is an instance of real number and number2 is an instance of real number and rel(number1,number2,value) holds,
then for all unit holds: if unit is an instance of unit of measure, then rel("number1 unit(s)","number2 unit(s)","value unit(s)") holds

(=>
      (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)))))