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Sigma KEE  AntisymmetricRelation
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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
.
Relationships
Parents
BinaryRelation
BinaryRelation
s are relations that are true only of pairs of things.
BinaryRelation
s are represented as slots in frame systems.
Children
AsymmetricRelation
A
BinaryRelation
is asymmetric if and only if it is both an
AntisymmetricRelation
and an
IrreflexiveRelation
.
PartialOrderingRelation
A
BinaryRelation
is a partial ordering if it is a
ReflexiveRelation
, an
AntisymmetricRelation
, and a
TransitiveRelation
.
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