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traditionalLogic
KB Term:
PartialOrderingRelation
Sigma KEE - PartialOrderingRelation
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半順序関係
BinaryRelation
は、
ReflexiveRelation
、
AntisymmetricRelation
、および
TransitiveRelation
の場合の部分的な 順序付けである。
Relationships
Parents
反対称関係
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
.
反射関係
Relation
?REL is reflexive iff (?REL ?INST ?INST) for all ?INST.
合計値関係
A
Relation
is a
TotalValuedRelation
just in case there exists an assignment for the last argument position of the
Relation
given any assignment of values to every argument position except the last one. Note that declaring a
Relation
to be both a
TotalValuedRelation
and a
SingleValuedRelation
means that it is a total function.
推移関係
A
BinaryRelation
?REL is transitive if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3.
Children
全順序関係
A
BinaryRelation
is a
TotalOrderingRelation
if it is a
PartialOrderingRelation
and a
TrichotomizingRelation
.
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