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Entity > Abstract > Class > Relation > BinaryRelation > BinaryPredicate > disjoint
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disjoint comparison table
Subject have domain2 have domain1 be first domain of documentation have axiom is a kind of is an instance of
BinaryPredicate  singleValuedA Predicate relating two items - its valence is two
(=>
 	(instance ?REL BinaryPredicate)
 	(valence ?REL 2))
Predicate 
SymmetricRelation  trichotomizingOnA BinaryRelation ?REL is symmetric just in case (?REL ?INST1 ?INST2) imples (?REL ?INST2 ?INST1), for all ?INST1 and ?INST2
(=>
    (instance ?REL SymmetricRelation)
    (forall (?INST1 ?INST2)
       (=>
          (holds ?REL ?INST1 ?INST2)
          (holds ?REL ?INST2 ?INST2))))
BinaryRelation 
disjointClassClasssingleValuedClasses are disjoint only if they share no instances, i.e. just in case the result of applying IntersectionFn to them is empty
(=>
    (instance ?SUPERCLASS PairwiseDisjointClass)
    (forall (?CLASS1 ?CLASS2)
       (=>
          (and
             (instance ?CLASS1 ?SUPERCLASS)
             (instance ?CLASS2 ?SUPERCLASS))
          (or
             (equal ?CLASS1 ?CLASS2)
             (disjoint ?CLASS1 ?CLASS2)))))
 SymmetricRelation

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