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Entity > Abstract > Class > Relation > BinaryRelation > BinaryPredicate > lessThan
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lessThan comparison table
Subject have domain2 have domain1 be first domain of be second domain of documentation 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 
RelationExtendedToQuantities  valencesubrelationA RelationExtendedToQuantities is a Relation that, when it is true on a sequence of arguments that are RealNumbers, it is also true on a sequence of ConstantQuantites with those magnitudes in some unit of measure. For example, the lessThan relation is extended to quantities. This means that for all pairs of quantities ?QUANTITY1 and ?QUANTITY2, (lessThan ?QUANTITY1 ?QUANTITY2) if and only if, for some ?NUMBER1, ?NUMBER2, and ?UNIT, ?QUANTITY1 = (MeasureFn ?NUMBER1 ?UNIT), ?QUANTITY2 = (MeasureFn ?NUMBER2 ?UNIT), and (lessThan ?NUMBER1 ?NUMBER2), for all units ?UNIT on which ?QUANTITY1 and ?QUANTITY2 can be measured. Note that, when a RelationExtendedToQuantities is extended from RealNumbers to ConstantQuantities, the ConstantQuantities must be measured along the same physical dimension
(=>
(and
(instance ?REL RelationExtendedToQuantities)
(instance ?REL BinaryRelation)
(instance ?NUMBER1 RealNumber)
(instance ?NUMBER2 RealNumber)
(holds ?REL ?NUMBER1 ?NUMBER2))
(forall (?UNIT)
(=>
(instance ?UNIT UnitOfMeasure)
(holds ?REL (MeasureFn ?NUMBER1 ?UNIT) (MeasureFn ?NUMBER2 ?UNIT)))))
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 
lessThanQuantityQuantityvalencesubrelation(lessThan ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is less than the Quantity ?NUMBER2
(=>
(instance ?NUMBER NegativeRealNumber)
(lessThan ?NUMBER 0))
 TransitiveRelation

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