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# （結合）價 (valence)

Specifies the number of arguments that a relation can take. If a relation does not have a fixed number of arguments, it does not have a valence and it is an instance of VariableArityRelation. For example, holds is a VariableArityRelation.

## Ontology

SUMO / STRUCTURAL-ONTOLOGY

 種類

可繼承關係

二元述詞
 不對稱關係
 種類

可繼承關係

單值關係

（結合）價

valence(關係, 正整數)

## Axioms (13)

If pred1pred2次關係 and pred1 %&有 論元(s) number, then pred2 %&有 論元(s) number.
```(=>
(and
(subrelation ?PRED1 ?PRED2)
(valence ?PRED1 ?NUMBER))
(valence ?PRED2 ?NUMBER))```

If 無交集關係() holds and rel1 是 "()" 的 一 成員 and rel2 是 "()" 的 一 成員 and rel1 %&有 論元(s) number, then rel2 %&有 論元(s) number.
```(=>
(and
(disjointRelation @ROW)
(inList
?REL1
(ListFn @ROW))
(inList
?REL2
(ListFn @ROW))
(valence ?REL1 ?NUMBER))
(valence ?REL2 ?NUMBER))```

rel全值關係實例 if and only if there exists valence so that rel關係實例 and rel %&有 論元(s) valence and
• if for all number,element,class holds: if number 小於 valence and rel 的 論元 numberclass實例 and element 等於 ""()" 的 第二 元素", then elementclass實例,
• then there exists item so that rel(,item) (不) 成立s
• .
```(<=>
(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))))))```

```(=>
(valence ?REL ?NUMBER)
(forall
(@ROW)
(=>
(holds ?REL @ROW)
(equal
(ListLengthFn
(ListFn @ROW))
?NUMBER))))```

If function一元函數實例, then function %&有 論元(s) .
```(=>
(instance ?FUNCTION UnaryFunction)
(valence ?FUNCTION 1))```

If function二元函數實例, then function %&有 論元(s) .
```(=>
(instance ?FUNCTION BinaryFunction)
(valence ?FUNCTION 2))```

If function三元函數實例, then function %&有 論元(s) .
```(=>
(instance ?FUNCTION TernaryFunction)
(valence ?FUNCTION 3))```

If function四元函數實例, then function %&有 論元(s) .
```(=>
(instance ?FUNCTION QuaternaryFunction)
(valence ?FUNCTION 4))```

If rel二元述詞實例, then rel %&有 論元(s) .
```(=>
(instance ?REL BinaryPredicate)
(valence ?REL 2))```

If rel三元述詞實例, then rel %&有 論元(s) .
```(=>
(instance ?REL TernaryPredicate)
(valence ?REL 3))```

If rel四元述詞實例, then rel %&有 論元(s) .
```(=>
(instance ?REL QuaternaryPredicate)
(valence ?REL 4))```

If rel五元述詞實例, then rel %&有 論元(s) .
```(=>
(instance ?REL QuintaryPredicate)
(valence ?REL 5))```

If rel變異元數關係實例, then there doesn't exist int so that rel %&有 論元(s) int.
```(=>
(instance ?REL VariableArityRelation)
(not
(exists
(?INT)
(valence ?REL ?INT))))```