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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > AsymmetricRelation > partialOrderingOn
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partialOrderingOn comparison table
Subject have domain2 have domain1 be first domain of documentation have axiom is a kind of is an instance of
AsymmetricRelation  trichotomizingOnA BinaryRelation is asymmetric only if it is both an AntisymmetricRelation and an IrreflexiveRelation
(=>
    (instance ?REL IrreflexiveRelation)
    (forall (?INST)
       (not 
          (holds ?REL ?INST ?INST))))
IrreflexiveRelation 
BinaryPredicate  singleValuedA Predicate relating two items - its valence is two
(=>
 	(instance ?REL BinaryPredicate)
 	(valence ?REL 2))
Predicate 
partialOrderingOnClassBinaryRelationsingleValuedA BinaryRelation is a partial ordering on a Class only if the relation is reflexiveOn the Class, and it is both an AntisymmetricRelation, and a TransitiveRelation
(=> 
    (partialOrderingOn ?RELATION ?CLASS)
    (and 
       (reflexiveOn ?RELATION ?CLASS)
       (instance ?RELATION TransitiveRelation)
       (instance ?RELATION AntisymmetricRelation)))
 BinaryPredicate

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