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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > AsymmetricRelation > trichotomizingOn
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trichotomizingOn 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 
trichotomizingOnClassBinaryRelationsingleValuedA BinaryRelation ?REL is trichotomizing on a Class only if, for all instances ?INST1 and ?INST2 of the Class, at least one of the following holds: (?REL ?INST1 ?INST2), (?REL ?INST2 ?INST1) or (equal ?INST1 ?INST2)
(=>
    (trichotomizingOn ?RELATION ?CLASS)
    (forall (?INST1 ?INST2)
       (=> 
          (and 
             (instance ?INST1 ?CLASS)
             (instance ?INST2 ?CLASS))
          (or 
             (holds ?RELATION ?INST1 ?INST2) 
             (holds ?RELATION ?INST2 ?INST1) 
             (equal ?INST1 ?INST2)))))
 BinaryPredicate

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