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  PartialOrderingRelation

 Sigma KEE - PartialOrderingRelation
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relation partiellement dirig�e
A BinaryRelation is a partial ordering if it is a ReflexiveRelation, an AntisymmetricRelation, and a TransitiveRelation.
Relationships      
Parents relation antisym�trique 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.
  relation r�flexive Relation ?REL is reflexive iff (?REL ?INST ?INST) for all ?INST.
  relation total 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.
  relation transitive A BinaryRelation ?REL is transitive if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3.
Children relation totalement dirig�eA BinaryRelation is a TotalOrderingRelation if it is a PartialOrderingRelation and a TrichotomizingRelation.


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