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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > AsymmetricRelation > closedOn
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closedOn 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 
closedOnClassFunctionsingleValuedA BinaryFunction is closed on a Class if it is defined for all instances of the Class and its value is always an instance of the Class
(=>
    (and
       (closedOn ?FUNCTION ?CLASS)
       (instance ?FUNCTION BinaryFunction))
    (forall (?INST1 ?INST2)
       (=> 
          (and 
             (instance ?INST1 ?CLASS) 
             (instance ?INST2 ?CLASS))
          (instance (AssignmentFn ?FUNCTION ?INST1 ?INST2) ?CLASS))))
 BinaryPredicate

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