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# 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

 實體

抽象的

關係

二元關係

可遞關係

## Axioms (3)

```(=>
(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可遞關係實例 and relation反對稱關係實例.
```(=>
(partialOrderingOn ?RELATION ?CLASS)
(and
(reflexiveOn ?RELATION ?CLASS)
(instance ?RELATION TransitiveRelation)
(instance ?RELATION AntisymmetricRelation)))```

If relation 等同關係class , then relation可遞關係實例 and relation對稱關係實例 and relation 反應於 class .
```(=>
(equivalenceRelationOn ?RELATION ?CLASS)
(and
(instance ?RELATION TransitiveRelation)
(instance ?RELATION SymmetricRelation)
(reflexiveOn ?RELATION ?CLASS)))```