PhysicalQuantity Comparison Table

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PhysicalQuantity comparison table

Subject be third domain of documentation be second domain of be first domain of have axiom

ConstantQuantity A ConstantQuantity is a PhysicalQuantity which has a constant value, e.g. 3 meters and 5 hours. The magnitude (see MagnitudeFn) of every ConstantQuantity is a RealNumber. ConstantQuantities are distinguished from FunctionQuantities, which map ConstantQuantities to other ConstantQuantities. All ConstantQuantites are expressed with the BinaryFunction MeasureFn, which takes a Number and a UnitOfMeasure as arguments. For example, 3 Meters can be expressed as (MeasureFn 3 Meter). ConstantQuantities form a partial order (see PartialOrderingRelation) with the lessThan relation, since lessThan is a RelationExtendedToQuantities and lessThan is defined over the RealNumbers. The lessThan relation is not a total order (see TotalOrderingRelation) over the class ConstantQuantity since elements of some subclasses of ConstantQuantity (such as length quantities) are incomparable to elements of other subclasses of ConstantQuantity (such as mass quantities) measure MagnitudeFn
(=>
(instance ?FUNCTION UnaryConstantFunctionQuantity)
(and
(domain ?FUNCTION 1 ConstantQuantity)
(range ?FUNCTION ConstantQuantity)))

FunctionQuantity domainSubclass A FunctionQuantity is a Function that maps from one or more instances of ConstantQuantity to another instance of ConstantQuantity. For example, the velocity of a particle would be represented by a FunctionQuantity mapping values of time (which are ConstantQuantities) to values of distance (also ConstantQuantities). Note that all instances of FunctionQuantity are Functions with a fixed arity. Note too that all elements of the range of a FunctionQuantity have the same physical dimension as the FunctionQuantity itself SubtractionFn rangeSubclass
(<=>
(instance ?ABS Abstract)
(not
(exists (?POINT)
(or
(located ?ABS ?POINT)
(existant ?ABS ?POINT)))))

UnitOfMeasure A standard of measurement for some dimension. For example, the Meter is a UnitOfMeasure for the dimension of length, as is the Inch. There is no intrisic property of a UnitOfMeasure that makes it primitive or fundamental; rather, a system-of-units (e.g. SystemeInternationalUnit) defines a set of orthogonal dimensions and assigns units for each MeasureFn SubtractionFn
(=>
(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)))))

Subject	be third domain of	documentation	be second domain of	be first domain of	have axiom
ConstantQuantity		A ConstantQuantity is a PhysicalQuantity which has a constant value, e.g. 3 meters and 5 hours. The magnitude (see MagnitudeFn) of every ConstantQuantity is a RealNumber. ConstantQuantities are distinguished from FunctionQuantities, which map ConstantQuantities to other ConstantQuantities. All ConstantQuantites are expressed with the BinaryFunction MeasureFn, which takes a Number and a UnitOfMeasure as arguments. For example, 3 Meters can be expressed as (MeasureFn 3 Meter). ConstantQuantities form a partial order (see PartialOrderingRelation) with the lessThan relation, since lessThan is a RelationExtendedToQuantities and lessThan is defined over the RealNumbers. The lessThan relation is not a total order (see TotalOrderingRelation) over the class ConstantQuantity since elements of some subclasses of ConstantQuantity (such as length quantities) are incomparable to elements of other subclasses of ConstantQuantity (such as mass quantities)	measure	MagnitudeFn	(=> (instance ?FUNCTION UnaryConstantFunctionQuantity) (and (domain ?FUNCTION 1 ConstantQuantity) (range ?FUNCTION ConstantQuantity)))
FunctionQuantity	domainSubclass	A FunctionQuantity is a Function that maps from one or more instances of ConstantQuantity to another instance of ConstantQuantity. For example, the velocity of a particle would be represented by a FunctionQuantity mapping values of time (which are ConstantQuantities) to values of distance (also ConstantQuantities). Note that all instances of FunctionQuantity are Functions with a fixed arity. Note too that all elements of the range of a FunctionQuantity have the same physical dimension as the FunctionQuantity itself	SubtractionFn	rangeSubclass	(<=> (instance ?ABS Abstract) (not (exists (?POINT) (or (located ?ABS ?POINT) (existant ?ABS ?POINT)))))
UnitOfMeasure		A standard of measurement for some dimension. For example, the Meter is a UnitOfMeasure for the dimension of length, as is the Inch. There is no intrisic property of a UnitOfMeasure that makes it primitive or fundamental; rather, a system-of-units (e.g. SystemeInternationalUnit) defines a set of orthogonal dimensions and assigns units for each	MeasureFn	SubtractionFn	(=> (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)))))

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