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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > AsymmetricRelation > CardinalityFn
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CardinalityFn 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 
UnaryFunction  rangeSubclassThe Class of Functions that require a single argument
(=>
    (instance ?FUNCTION UnaryFunction)
    (valence ?FUNCTION 1))
Function 
CardinalityFnNonnegativeInteger(UnionFn Class Collection)rangeSubclass(CardinalityFn ?CLASS) returns the number of instances in the Class or Collection ?CLASS
(=>
    (instance ?SET FiniteSet)
    (exists (?NUMBER)
       (and
          (instance ?NUMBER NonnegativeInteger)
          (equal ?NUMBER (CardinalityFn ?SET)))))
 UnaryFunction

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