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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > AsymmetricRelation > element
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element 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 
IntransitiveRelation  trichotomizingOnA BinaryRelation ?REL is intransitive only if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply not (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3
(=> 
    (instance ?REL IntransitiveRelation)
    (forall (?INST1 ?INST2 ?INST3)
       (=> 
          (and 
             (holds ?REL ?INST1 ?INST2)
             (holds ?REL ?INST2 ?INST3))
          (not 
             (holds ?REL ?INST1 ?INST3)))))
BinaryRelation 
elementSetEntitysingleValued(element ?ENTITY ?SET) is true just in case ?ENTITY is contained in the Set ?SET. An Entity can be an element of another Entity only if the latter is a Set
(=>
    (forall (?ELEMENT)
          (<=>
             (element ?ELEMENT ?SET1)
             (element ?ELEMENT ?SET2)))
    (equal ?SET1 ?SET2))
 IntransitiveRelation

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