關係 (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

Superclass(es)

實體

抽象的

關係

Subclass(es)

單值關係全值關係偏值關係二元關係或然率關係空間關係時間關係三元關係四元關係五元關係序列述詞變異元數關係與量關係

Coordinate term(s)

屬性圖圖元件命題數量集合或種類

Constrains relations

領域領域次種類成立次關係（結合）價

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 無交集關係() holds and rel 是 "()" 的一成員, then rel 是關係的實例.

(=>
      (and
            (disjointRelation @ROW)
            (inList
                  ?REL
                  (ListFn @ROW)))
      (instance ?REL Relation))

關係無交集地分解成二元關係,三元關係,四元關係,五元關係,變異元數關係.

(disjointDecomposition Relation BinaryRelation TernaryRelation QuaternaryRelation QuintaryRelation VariableArityRelation)

關係完全分割成述詞,函數,序列.

(partition Relation Predicate Function List)

關係完全分割成全值關係,偏值關係.

(partition Relation TotalValuedRelation PartialValuedRelation)

If rel 是關係的實例, then rel() (不) 成立s if and only if rel() holds.

(=>
      (instance ?REL Relation)
      (<=>
            (holds ?REL @ROW)
            (?REL @ROW)))

rel 是全值關係的實例 if and only if there exists valence so that rel 是關係的實例 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 number 是 class 的實例 and element 等於 ""()" 的第二元素", then element 是 class 的實例,
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))))))