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  PartialOrderingRelation

 Sigma KEE - PartialOrderingRelation
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PartialOrderingRelation
A BinaryRelation is a partial ordering if it is a ReflexiveRelation, an AntisymmetricRelation, and a TransitiveRelation.
Relationships      
Parents 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.
  ReflexiveRelation Relation ?REL is reflexive iff (?REL ?INST ?INST) for all ?INST.
  TotalValuedRelation 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.
  TransitiveRelation A BinaryRelation ?REL is transitive if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3.
Children TotalOrderingRelationA BinaryRelation is a TotalOrderingRelation if it is a PartialOrderingRelation and a TrichotomizingRelation.


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