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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > AsymmetricRelation > identityElement
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identityElement 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 
identityElementEntityBinaryFunctionsingleValuedAn object ?ID is the identity element for BinaryFunction ?FUNCTION just in case, for every instance ?INST, applying ?FUNCTION to ?INST and ?ID results in ?INST
(=>
    (identityElement ?FUNCTION ?ID)
    (forall (?INST)
       (=>
          (instance ?INST (DomainFn ?FUNCTION))
          (equal (AssignmentFn ?FUNCTION ?ID ?INST) ?INST))))
 BinaryPredicate

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