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# relation (Relation)

The Class of relations. There are three kinds of Relation: Predicate, Function, and List. Predicates and Functions both denote sets of ordered n-tuples. The difference between these two Classes is that Predicates cover formula-forming operators, while Functions cover term-forming operators. A List, on the other hand, is a particular ordered n-tuple.

## Ontology

SUMO / BASE-ONTOLOGY

 entity

abstract

relation

## Subclass(es)

single valued relation  total valued relation  partial valued relation  binary relation  probability relation  spatial relation  temporal relation  ternary relation  quaternary relation  quintary relation  list  predicate  variable arity relation  relation extended to quantities

## Coordinate term(s)

attribute  graph  graph element  proposition  quantity  set or class

## Constrains relations

domain  domain subclass  holds  subrelation  valence

## Related WordNet synsets

relation
an abstraction belonging to or characteristic of two entities or parts together

relationship, human relationship
(`relationship' is often used where `relation' would serve (as in "the relationship between inflation and unemployment")) preferred usage of `relationship' is for human relations or states of relatedness; "the relationship between mothers and children"

relational
having a relation or being related

See more related synsets on a separate page.

## Axioms (6)

If and ? are disjoint and rel is a member of "()", then rel is an instance of relation.
```(=>
(and
(disjointRelation @ROW)
(inList
?REL
(ListFn @ROW)))
(instance ?REL Relation))```

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

relation is exhaustively partitioned into predicate,function,list.
`(partition Relation Predicate Function List)`

relation is exhaustively partitioned into total valued relation,partial valued relation.
`(partition Relation TotalValuedRelation PartialValuedRelation)`

If rel is an instance of relation, then rel() holds if and only if rel() holds.
```(=>
(instance ?REL Relation)
(<=>
(holds ?REL @ROW)
(?REL @ROW)))```

rel is an instance of total valued relation if and only if there exists valence so that rel is an instance of relation and rel %&has valence argument(s) and
• if for all number,element,class holds: if number is less than valence and the number number argument of rel is an instance of class and element is equal to "numberth element of "()"", then element is an instance of class,
• then there exists item so that rel(,item) holds
• .
```(<=>
(instance ?REL TotalValuedRelation)
(exists
(?VALENCE)
(and
(instance ?REL Relation)
(valence ?REL ?VALENCE)
(=>
(forall
(?NUMBER ?ELEMENT ?CLASS)
(=>
(and
(lessThan ?NUMBER ?VALENCE)
(domain ?REL ?NUMBER ?CLASS)
(equal
?ELEMENT
(ListOrderFn
(ListFn @ROW)
?NUMBER)))
(instance ?ELEMENT ?CLASS)))
(exists
(?ITEM)
(holds ?REL @ROW ?ITEM))))))```