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Entity > Abstract > Class > Relation > BinaryRelation > AntisymmetricRelation > AsymmetricRelation > on
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on 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))))
IntransitiveRelation A BinaryRelation ?REL is intransitive only if (?REL ?INST1 ?INST2) and (?REL ?INST2 ?INST3) imply not (?REL ?INST1 ?INST3), for all ?INST1, ?INST2, and ?INST3BinaryRelation
(=> 
    (instance ?REL IntransitiveRelation)
    (forall (?INST1 ?INST2 ?INST3)
       (=> 
          (and 
             (holds ?REL ?INST1 ?INST2)
             (holds ?REL ?INST2 ?INST3))
          (not 
             (holds ?REL ?INST1 ?INST3)))))
onIntransitiveRelationThis is a cognitive primitive, derived from the up/down schema and involving contact. (on ?OBJ1 ?OBJ2) means that ?OBJ1 is on top of ?OBJ2 
(=>
   (under ?OBJ1 ?OBJ2)
   (or
     (on ?OBJ2 ?OBJ1)
     (above ?OBJ2 ?OBJ1)))

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