greaterThan Comparison Table

Entity > Abstract > Class > Relation > BinaryRelation > BinaryPredicate > greaterThan

Next BinaryPredicate: greaterThanOrEqualTo Up: BinaryPredicate, IrreflexiveRelation, RelationExtendedToQuantities, TransitiveRelation Previous BinaryPredicate: frequency

greaterThan 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 singleValued inverse A Predicate relating two items - its valence is two
(=>
(instance ?REL BinaryPredicate)
(valence ?REL 2))
Predicate

IrreflexiveRelation trichotomizingOn inverse Relation ?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 valence subrelation A 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 trichotomizingOn inverse A 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

greaterThan Quantity Quantity valence subrelation (greaterThan ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is greater than the Quantity ?NUMBER2 lessThan
(=>
(larger ?OBJ1 ?OBJ2)
(forall (?QUANT1 ?QUANT2)
(=>
(and
(measure ?OBJ1 (MeasureFn ?QUANT1 LengthMeasure))
(measure ?OBJ2 (MeasureFn ?QUANT2 LengthMeasure)))
(greaterThan ?QUANT1 ?QUANT2))))
TransitiveRelation

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			singleValued	inverse	A Predicate relating two items - its valence is two		(=> (instance ?REL BinaryPredicate) (valence ?REL 2))	Predicate
IrreflexiveRelation			trichotomizingOn	inverse	Relation ?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			valence	subrelation	A 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			trichotomizingOn	inverse	A 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
greaterThan	Quantity	Quantity	valence	subrelation	(greaterThan ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is greater than the Quantity ?NUMBER2	lessThan	(=> (larger ?OBJ1 ?OBJ2) (forall (?QUANT1 ?QUANT2) (=> (and (measure ?OBJ1 (MeasureFn ?QUANT1 LengthMeasure)) (measure ?OBJ2 (MeasureFn ?QUANT2 LengthMeasure))) (greaterThan ?QUANT1 ?QUANT2))))		TransitiveRelation

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