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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > AsymmetricRelation > precondition
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precondition 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 
TransitiveRelation  trichotomizingOnA BinaryRelation ?REL is transitive if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3
(=>
    (instance ?REL TransitiveRelation)
    (forall (?INST1 ?INST2 ?INST3)
       (=>
          (and
             (holds ?REL ?INST1 ?INST2)
             (holds ?REL ?INST2 ?INST3))
          (holds ?REL ?INST1 ?INST3))))
BinaryRelation 
preconditionProcessProcesssingleValuedA very general Predicate. (precondition ?PROC1 ?PROC2) means that ?PROC2 can exist or be true only if ?PROC1 exists or is true. At some point, this Predicate should probably be broken up into more specific Predicates with more restrictive domain restrictions
(=>
    (instance ?REL TransitiveRelation)
    (forall (?INST1 ?INST2 ?INST3)
       (=>
          (and
             (holds ?REL ?INST1 ?INST2)
             (holds ?REL ?INST2 ?INST3))
          (holds ?REL ?INST1 ?INST3))))
 TransitiveRelation

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