反對稱關係 (AntisymmetricRelation)

BinaryRelation rel is an AntisymmetricRelation if for distinct inst1 and inst2, (rel inst1 inst2) implies not (rel inst2 inst1). In other words, for all inst1 and inst2, (rel inst1 inst2) and (rel inst2 inst1) imply that inst1 and inst2 are identical. Note that it is possible for an AntisymmetricRelation to be a ReflexiveRelation.

Ontology

SUMO / BASE-ONTOLOGY

Superclass(es)

實體

抽象的

關係

二元關係

反對稱關係

Subclass(es)

不對稱關係偏序關係

Coordinate term(s)

二元述詞非可遞關係非反身關係反身關係對稱關係可遞關係三角關係一元函數

Axioms (2)

if rel 是反對稱關係的實例,
then for all inst1,inst2 holds: if rel(inst1,inst2) (不) 成立s and rel(inst2,inst1) (不) 成立s, then inst1 等於 inst2

(=>
      (instance ?REL AntisymmetricRelation)
      (forall
            (?INST1 ?INST2)
            (=>
                  (and
                        (holds ?REL ?INST1 ?INST2)
                        (holds ?REL ?INST2 ?INST1))
                  (equal ?INST1 ?INST2))))

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)))