PhysicalQuantity

Sigma KEE - PhysicalQuantity
PhysicalQuantity
A PhysicalQuantity is a measure of some quantifiable aspect of the modeled world, such as 'the earth's diameter' (a constant length) and 'the stress in a loaded deformable solid' (a measure of stress, which is a function of three spatial coordinates). Every PhysicalQuantity is either a ConstantQuantity or FunctionQuantity . Instances of ConstantQuantity are dependent on a UnitOfMeasure , while instances of FunctionQuantity are Function s that map instances of ConstantQuantity to other instances of ConstantQuantity (e.g., a TimeDependentQuantity is a FunctionQuantity ). Although the name and definition of PhysicalQuantity is borrowed from physics, a PhysicalQuantity need not be material. Aside from the dimensions of length, time, velocity, etc., nonphysical dimensions such as currency are also possible. Accordingly, amounts of money would be instances of PhysicalQuantity . A PhysicalQuantity is distinguished from a pure Number by the fact that the former is associated with a dimension of measurement.

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Quantity
Any specification of how many or how much of something there is. Accordingly, there are two subclasses of Quantity : Number (how many) and PhysicalQuantity (how much).
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ConstantQuantity A ConstantQuantity is a PhysicalQuantity that has a constant value, e.g. 3 Meter s and 5 HourDuration s. The magnitude (see MagnitudeFn ) of every ConstantQuantity is a RealNumber . ConstantQuantity is distinguished from FunctionQuantity , in that each instance of the latter is formed through the mapping of one PhysicalQuantity to another PhysicalQuantity . Each instance of ConstantQuantity is expressed with the BinaryFunction MeasureFn , which takes a Number and a UnitOfMeasure as arguments. For example, 3 Meter s is expressed as (MeasureFn 3 Meter ). Instances of ConstantQuantity form a partial order (see PartialOrderingRelation ) with the lessThan relation, since lessThan is a RelationExtendedToQuantities and lessThan is defined over the RealNumber s. 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). FunctionQuantity A FunctionQuantity is a PhysicalQuantity that is returned by 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 relating values of time (which are instances of ConstantQuantity ) to values of distance (also instances of ConstantQuantity ). Note that all elements of the range of the Function corresponding to a FunctionQuantity have the same physical dimension as the FunctionQuantity itself. PerformanceMeasure 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 intrinsic 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.

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