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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > AsymmetricRelation > equivalenceRelationOn
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equivalenceRelationOn 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 
equivalenceRelationOnClassBinaryRelationsingleValuedA BinaryRelation is an equivalenceRelationOn a Class only if the relation is reflexiveOn the Class and it is both a TransitiveRelation and a SymmetricRelation
(=>
    (equivalenceRelationOn ?RELATION ?CLASS)
    (and
       (instance ?RELATION TransitiveRelation)
       (instance ?RELATION SymmetricRelation)
       (reflexiveOn ?RELATION ?CLASS)))
 BinaryPredicate

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