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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation
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AntisymmetricRelationdocumentation 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 ReflexiveRelation2001-11-30 13:33:37.0
has axiom
(partialOrderingOn ?RELATION ?CLASS)
(reflexiveOn ?RELATION ?CLASS)
(instance ?RELATION TransitiveRelation)
(instance ?RELATION AntisymmetricRelation)))
2001-11-30 13:33:37.0
has axiom
(instance ?REL AntisymmetricRelation)
(forall (?INST1 ?INST2)
(holds ?REL ?INST1 ?INST2)
(holds ?REL ?INST2 ?INST1))
(equal ?INST1 ?INST2))))
2001-11-30 13:33:37.0
is a kind of BinaryRelation2001-11-30 13:33:37.0
BinaryRelationis first domain of DomainFn2001-11-30 13:33:44.0
is first domain of equivalenceRelationOn2001-11-30 13:33:44.0
is first domain of inverse2001-11-30 13:33:44.0
is first domain of irreflexiveOn2001-11-30 13:33:44.0
is first domain of partialOrderingOn2001-11-30 13:33:44.0
is first domain of RangeFn2001-11-30 13:33:44.0
is first domain of reflexiveOn2001-11-30 13:33:44.0
is first domain of totalOrderingOn2001-11-30 13:33:44.0
is first domain of trichotomizingOn2001-11-30 13:33:44.0
is second domain of inverse2001-11-30 13:33:44.0
Classis third domain of domain2001-11-30 13:33:51.0
is third domain of domainSubclass2001-11-30 13:33:51.0
Abstractis disjoint from Physical2001-11-30 13:33:32.0

Kinds of AntisymmetricRelation :

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