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Entity > Abstract > Class > Relation > BinaryRelation > BinaryPredicate > smaller
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smaller comparison table
Subject have domain2 have domain1 be first domain of be second domain of documentation have inverse have axiom is a kind of is an instance of
BinaryPredicate  singleValuedinverseA Predicate relating two items - its valence is two 
(=>
(instance ?REL BinaryPredicate)
(valence ?REL 2))
Predicate 
IrreflexiveRelation  trichotomizingOninverseRelation ?REL is irreflexive if (?REL ?INST ?INST) holds for no value of ?INST 
(=>
(instance ?REL IrreflexiveRelation)
(forall (?INST)
(not
(holds ?REL ?INST ?INST))))
BinaryRelation 
SpatialRelation  valencesubrelationThe Class of Relations that are spatial in a wide sense. This Class includes mereological relations, topological relations, and positional relations 
(=>
(and
(instance ?REL SpatialRelation)
(holds ?REL ?OBJ1 ?OBJ2))
(overlapsTemporally (WhenFn ?OBJ1) (WhenFn ?OBJ2)))
Relation 
TransitiveRelation  trichotomizingOninverseA 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 
smallerObjectObjectvalencesubrelation(smaller ?OBJ1 ?OBJ2) simply means that ?OBJ1 is smaller, with respect to all LengthMeasures, than ?OBJ2larger
(=>
(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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