Formally speaking, AS6969™ defines basic quantities and their possible value structures. The basic quantities defined are cardinal quantities, which have algebraic significance. The ‘conceptual’ definition of a cardinal quantity includes its innate quantity equation, which is tied to the base quantities or ‘dimensions’ of a system of quantities. These definitions are fully conformant to ISO/IEC 80000.
For scalars, the possible value structures are given by their valid measurement units. Consider length. The length values of 2.54 cm and 1 inch have the same mathematical value (magnitude) but different structures. The specification of the scientifically-arbitrary measurement unit is called the ‘logical’ specification.
For vectors, their direction in ordinary space also has a value structure, which is determined by a scientifically-arbitrary coordinate reference system (CRS). Each coordinate can then be assigned a measurement unit to complete the logical specification of the vector.
In higher mathematics, the structure of vector spaces is considered an ordinary category, which is one of many ordinary categories in mathematics. This is dealt with in Category Theory. Thus, in principle, other categories of value structure could be added to AS6969™ if of practical utility.
Going beyond AS6969™ it is possible to define other kinds of quantity that are of empirical relevance. These are relative quantities (the ratio of a cardinal quantity to a reference value, such as percentage volume) and ordinal quantities (dimensionless quantities based on an arbitrary test method and scale, such as gasoline octane rating). It is also possible to define function parameters, such as a device’s sensitivity or gain setting. Finally, an enumeration of quality values could be defined for a particular purpose.
It is expected that these would be defined in a quantity domain.
In data modeling, it is convenient to arbitrarily distinguish between a quantity and a measurand, where a quantity can be represented by a property type (such as a UML attribute type) and a measurand can be represented by a property and its owner (such a UML class and its owned attribute). For example, we have the measurand ‘Aircraft:: grossTakeOffWeight: Mass (kg)’, where the quantity is ‘Mass (kg)’.
AS6969™ formally defines a measurand as:
The particular quantity subject to measurement. NOTE: The measurand comprises the general quantity to be measured and the specification of the phenomenon, body or substance that is the subject of the measurement.
All measurands are to be defined in quantity domains using the reference table provided in AS6969™. Where required in a quantity domain, and only where required, a measurand specification can be subsetted into a measurement specification, which can exist at different levels of detail. AS6969™ formally defines a measurement as:
The set of operations having the object of determining a value of a quantity.
For example, there could be multiple ways of determining aircraft gross take off weight, each yielding a different mass value. Another example is the measurand ‘aircraft altitude’, which could be subsetted into the measurements of barometric altitude, radar altitude, GPS altitude, and so on. The measurement reference table in AS6969™ allows for three increasing levels of detail following JCGM 100:2008. These are the principle of measurement, the method of measurement, and the measurement procedure.