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  PartialOrderingRelation

Sigma KEE - PartialOrderingRelation
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半順序関係
BinaryRelation は、 ReflexiveRelationAntisymmetricRelation、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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