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Entity > Abstract > Class > Relation > RelationExtendedToQuantities

RelationExtendedToQuantities
subject			fact

RelationExtendedToQuantities	documentation 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
	has axiom (=> (and (instance ?FUNCTION RelationExtendedToQuantities) (instance ?FUNCTION BinaryFunction) (instance ?NUMBER1 RealNumber) (instance ?NUMBER2 RealNumber) (equal (AssignmentFn ?FUNCTION ?NUMBER1 ?NUMBER2) ?VALUE)) (forall (?UNIT) (=> (instance ?UNIT UnitOfMeasure) (equal (AssignmentFn ?FUNCTION (MeasureFn ?NUMBER1 ?UNIT) (MeasureFn ?NUMBER2 ?UNIT)) (MeasureFn ?VALUE ?UNIT)))))
	has axiom (=> (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)))))
	is a kind of Relation
Relation	is first domain of domain
	is first domain of domainSubclass
	is first domain of holds
	is first domain of subrelation
	is first domain of valence
	is second domain of subrelation
Class	is third domain of domain
	is third domain of domainSubclass
Abstract	is disjoint from Physical

Kinds of RelationExtendedToQuantities :

• AdditionFn (9 facts) - If ?NUMBER1 and ?NUMBER2 are Numbers, then (AdditionFn ?NUMBER1 ?NUMBER2) is the arithmetical sum of these numbers
• DivisionFn (15 facts) - If ?NUMBER1 and ?NUMBER2 are Numbers, then (DivisionFn ?NUMBER1 ?NUMBER2) is the result of dividing ?NUMBER1 by ?NUMBER2. An exception occurs when ?NUMBER1 = 1, in which case (DivisionFn ?NUMBER1 ?NUMBER2) is the reciprocal of ?NUMBER2
• equal (6 facts) - (equal ?ENTITY1 ?ENTITY2) is true just in case ?ENTITY1 is identical with ?ENTITY2
• ExponentiationFn (7 facts) - (ExponentiationFn ?NUMBER ?INT) returns the RealNumber ?NUMBER raised to the power of the Integer ?INT
• greaterThan (16 facts) - (greaterThan ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is greater than the Quantity ?NUMBER2
• greaterThanOrEqualTo (11 facts) - (greaterThanOrEqualTo ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is greater than the Quantity ?NUMBER2
• lessThan (20 facts) - (lessThan ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is less than the Quantity ?NUMBER2
• lessThanOrEqualTo (10 facts) - (lessThanOrEqualTo ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is less than or equal to the Quantity ?NUMBER2
• MaxFn (8 facts) - (MaxFn ?NUMBER1 ?NUMBER2) is the largest of ?NUMBER1 and ?NUMBER2. In cases where ?NUMBER1 is equal to ?NUMBER2, MaxFn returns one of its arguments
• MinFn (8 facts) - (MinFn ?NUMBER1 ?NUMBER2) is the smallest of ?NUMBER1 and ?NUMBER2. In cases where ?NUMBER1 is equal to ?NUMBER2, MinFn returns one of its arguments
• MultiplicationFn (52 facts) - If ?NUMBER1 and ?NUMBER2 are Numbers, then (MultiplicationFn ?NUMBER1 ?NUMBER2) is the arithmetical product of these numbers
• ReciprocalFn (7 facts) - (ReciprocalFn ?NUMBER) is the reciprocal element of ?NUMBER with respect to the multiplication operator (MultiplicationFn), i.e. 1/?NUMBER. Not all numbers have a reciprocal element. For example the number 0 does not. If a number ?NUMBER has a reciprocal ?RECIP, then the product of ?NUMBER and ?RECIP will be 1, e.g. 3*1/3 = 1. The reciprocal of an element is equal to applying the ExponentiationFn function to the element to the power -1
• RemainderFn (11 facts) - (RemainderFn ?NUMBER ?DIVISOR) is the remainder of the number ?NUMBER divided by the number ?DIVISOR. The result has the same sign as ?DIVISOR
• RoundFn (6 facts) - (RoundFn ?NUMBER) is the Integer closest to ?NUMBER on the number line. If ?NUMBER is halfway between two Integers (for example 3.5), it denotes the larger Integer
• SubtractionFn (10 facts) - If ?NUMBER1 and ?NUMBER2 are Numbers, then (SubtractionFn ?NUMBER1 ?NUMBER2) is the arithmetical difference between ?NUMBER1 and ?NUMBER2, i.e. ?NUMBER1 minus ?NUMBER2. An exception occurs when ?NUMBER1 is equal to 0, in which case (SubtractionFn ?NUMBER1 ?NUMBER2) is the negation of ?NUMBER2