可遞關係 (TransitiveRelation)

A BinaryRelation rel is transitive if (rel inst1 inst2) and (rel inst2 inst3) imply (rel inst1 inst3), for all inst1, inst2, and inst3.

Ontology

SUMO / BASE-ONTOLOGY

Superclass(es)

實體

抽象的

關係

二元關係

可遞關係

Instance(s)

封閉續接屬性正部分次聚集小於大於相交先決條件次命題次計畫次圖大於小於開始完成先於期間較早外表部分內部發展期形式人造物版本次組織

Subclass(es)

偏序關係等同關係

Coordinate term(s)

反對稱關係二元述詞非可遞關係非反身關係反身關係對稱關係三角關係一元函數

Axioms (3)

if rel 是可遞關係的實例,
then for all inst1,inst2,inst3 holds: if rel(inst1,inst2) (不) 成立s and rel(inst2,inst3) (不) 成立s, then rel(inst1,inst3) (不) 成立s

(=>
      (instance ?REL TransitiveRelation)
      (forall
            (?INST1 ?INST2 ?INST3)
            (=>
                  (and
                        (holds ?REL ?INST1 ?INST2)
                        (holds ?REL ?INST2 ?INST3))
                  (holds ?REL ?INST1 ?INST3))))

If relation 偏序於 class, then relation 反應於 class and relation 是可遞關係的實例 and relation 是反對稱關係的實例.

(=>
      (partialOrderingOn ?RELATION ?CLASS)
      (and
            (reflexiveOn ?RELATION ?CLASS)
            (instance ?RELATION TransitiveRelation)
            (instance ?RELATION AntisymmetricRelation)))

If relation 等同關係於 class , then relation 是可遞關係的實例 and relation 是對稱關係的實例 and relation 反應於 class .

(=>
      (equivalenceRelationOn ?RELATION ?CLASS)
      (and
            (instance ?RELATION TransitiveRelation)
            (instance ?RELATION SymmetricRelation)
            (reflexiveOn ?RELATION ?CLASS)))