AntisymmetricRelation concept from the SUMO knowledge base

Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation

Next BinaryRelation: BinaryPredicate Up: BinaryRelation Previous BinaryRelation: UnaryFunction

AntisymmetricRelation

subject fact

AntisymmetricRelation documentation 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 2001-11-30 13:33:37.0
has axiom
(=>
(partialOrderingOn ?RELATION ?CLASS)
(and
(reflexiveOn ?RELATION ?CLASS)
(instance ?RELATION TransitiveRelation)
(instance ?RELATION AntisymmetricRelation)))
has axiom
(=>
(instance ?REL AntisymmetricRelation)
(forall (?INST1 ?INST2)
(=>
(and
(holds ?REL ?INST1 ?INST2)
(holds ?REL ?INST2 ?INST1))
(equal ?INST1 ?INST2))))
2001-11-30 13:33:37.0
is a kind of BinaryRelation

BinaryRelation is first domain of DomainFn 2001-11-30 13:33:44.0
is first domain of equivalenceRelationOn
is first domain of inverse
is first domain of irreflexiveOn
is first domain of partialOrderingOn
is first domain of RangeFn
is first domain of reflexiveOn
is first domain of totalOrderingOn 2001-11-30 13:33:44.0
is first domain of trichotomizingOn
is second domain of inverse

Class is third domain of domain 2001-11-30 13:33:51.0
is third domain of domainSubclass

Abstract is disjoint from Physical 2001-11-30 13:33:32.0

Kinds of AntisymmetricRelation :

AsymmetricRelation (81 kinds, 626 facts) - A BinaryRelation is asymmetric only if it is both an AntisymmetricRelation and an IrreflexiveRelation
instance (5 facts) - An object is an instance a Class if it is a member of that Class. An individual may be an instance of many classes, some of which may be subclasses of others. Thus, there is no assumption in the meaning of instance about specificity or uniqueness
PartialOrderingRelation (13 kinds, 186 facts) - A BinaryRelation is a partial ordering if it is a ReflexiveRelation, an AntisymmetricRelation, and a TransitiveRelation

Next BinaryRelation: BinaryPredicate Up: BinaryRelation Previous BinaryRelation: UnaryFunction

AntisymmetricRelation	*documentation* 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
	has axiom (=> (partialOrderingOn ?RELATION ?CLASS) (and (reflexiveOn ?RELATION ?CLASS) (instance ?RELATION TransitiveRelation) (instance ?RELATION AntisymmetricRelation)))
	has axiom (=> (instance ?REL AntisymmetricRelation) (forall (?INST1 ?INST2) (=> (and (holds ?REL ?INST1 ?INST2) (holds ?REL ?INST2 ?INST1)) (equal ?INST1 ?INST2))))
	is a kind of BinaryRelation
BinaryRelation	*is first domain* of** DomainFn
	*is first domain* of** equivalenceRelationOn
	*is first domain* of** inverse
	*is first domain* of** irreflexiveOn
	*is first domain* of** partialOrderingOn
	*is first domain* of** RangeFn
	*is first domain* of** reflexiveOn
	*is first domain* of** totalOrderingOn
	*is first domain* of** trichotomizingOn
	*is second domain* of** inverse
Class	*is third domain* of** domain
Class	*is third domain* of** domainSubclass
Abstract	*is disjoint* from** Physical