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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > AsymmetricRelation > under
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under comparison table
Subject is an instance of documentation is a kind of have axiom
AsymmetricRelation A BinaryRelation is asymmetric only if it is both an AntisymmetricRelation and an IrreflexiveRelationIrreflexiveRelation
(=>
    (instance ?REL IrreflexiveRelation)
    (forall (?INST)
       (not 
          (holds ?REL ?INST ?INST))))
TransitiveRelation A BinaryRelation ?REL is transitive if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3BinaryRelation
(=>
    (instance ?REL TransitiveRelation)
    (forall (?INST1 ?INST2 ?INST3)
       (=>
          (and
             (holds ?REL ?INST1 ?INST2)
             (holds ?REL ?INST2 ?INST3))
          (holds ?REL ?INST1 ?INST3))))
underTransitiveRelationThis is a cognitive primitive, derived from the up/down schema. (under ?OBJ1 ?OBJ2) means that ?OBJ1 is under ?OBJ2 
(=>
   (under ?OBJ1 ?OBJ2)
   (or
     (on ?OBJ2 ?OBJ1)
     (above ?OBJ2 ?OBJ1)))

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