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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > AsymmetricRelation > totalOrderingOn
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totalOrderingOn 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 
totalOrderingOnClassBinaryRelationsingleValuedA BinaryRelation ?REL is a total ordering on a Class only if it is a partial ordering for which either (?REL ?INST1 ?INST2) or (?REL ?INST2 ?INST1) for every ?INST1 and ?INST2 in the Class
(<=> 
      (totalOrderingOn ?RELATION ?CLASS)
      (and 
           (partialOrderingOn ?RELATION ?CLASS)
           (trichotomizingOn ?RELATION ?CLASS)))
 BinaryPredicate

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