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# total valued relation (TotalValuedRelation)

A Relation is a TotalValuedRelation just in case there exists an assignment for the last argument position of the Relation given any assignment of values to every argument position except the last one. Note that declaring a Relation to be both a TotalValuedRelation and a SingleValuedRelation means that it is a total function.

## Ontology

SUMO / BASE-ONTOLOGY

## Superclass(es)

 entity

abstract

relation

total valued relation

duration

## Coordinate term(s)

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

## Axioms (2)

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

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))))))```