equal Comparison Table

Entity > Abstract > Class > Relation > BinaryRelation > BinaryPredicate > equal

Next BinaryPredicate: equivalenceRelationOn Up: BinaryPredicate, EquivalenceRelation, RelationExtendedToQuantities Previous BinaryPredicate: element

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

EquivalenceRelation trichotomizingOn inverse A BinaryRelation is an equivalence relation if it is a ReflexiveRelation, a SymmetricRelation, and a TransitiveRelation
(=>
(instance ?REL TransitiveRelation)
(forall (?INST1 ?INST2 ?INST3)
(=>
(and
(holds ?REL ?INST1 ?INST2)
(holds ?REL ?INST2 ?INST3))
(holds ?REL ?INST1 ?INST3))))
TransitiveRelation

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

equal Entity Entity valence subrelation (equal ?ENTITY1 ?ENTITY2) is true just in case ?ENTITY1 is identical with ?ENTITY2
(=>
(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)))))
RelationExtendedToQuantities

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			singleValued	inverse	A Predicate relating two items - its valence is two	(=> (instance ?REL BinaryPredicate) (valence ?REL 2))	Predicate
EquivalenceRelation			trichotomizingOn	inverse	A BinaryRelation is an equivalence relation if it is a ReflexiveRelation, a SymmetricRelation, and a TransitiveRelation	(=> (instance ?REL TransitiveRelation) (forall (?INST1 ?INST2 ?INST3) (=> (and (holds ?REL ?INST1 ?INST2) (holds ?REL ?INST2 ?INST3)) (holds ?REL ?INST1 ?INST3))))	TransitiveRelation
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
equal	Entity	Entity	valence	subrelation	(equal ?ENTITY1 ?ENTITY2) is true just in case ?ENTITY1 is identical with ?ENTITY2	(=> (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)))))		RelationExtendedToQuantities

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