In AS6969™, a categorical value is an observable state at that instant that can be determined by measurement without context or other a-priori knowledge. The terms ‘modality’ and ‘modal’ are borrowed from modal logic. In linguistics, modal verbs include ‘can’, ‘could’, ‘may’, ‘might’, ‘must’, ‘should’, and ‘will’. In AS6969™, a quantity modal is a logical or mathematical operator that modifies the truth semantics of a quantity value, and a modality is a system of related modals.
Four modalities are addressed in AS6969™. They are alethic, deontic, metrological, and waveform. Other modalities could also be added if required in cyber physical systems.
Consider the measurand ‘Aircraft:: grossTakeOffWeight: Mass (kg)’, which concerns the state of the aircraft at take off. However, we might also be interested in the planned value (determined by the mission), the permissible values (for safe take off), and the uncertainty of the value. These are examples of modals. Modals can be expressed in two ways – either in the owned property or in the property type. Consider these examples using an arbitrary syntax:
Aircraft:: grossTakeOffWeight(permissible_max): Mass (kg)
Aircraft:: grossTakeOffWeight: MassState, where MassState includes the predicate MassState:: Mass(permissible_max): Mass (kg)
In both cases, ‘permissible_max’ is the modal operator. The second example could be architecturally elegant if MassState has multiple properties, including the categorical value, the uncertainty of the categorical value, and so on.
Alethic quantities are concerned with necessity and possibility. AS6969™ provides the example of an aircraft with a fuel capacity of 100 liters. A minimum fuel load of 5 liters is required to maintain the fuel flow specification under all flight-envelope conditions. Therefore, the range of possible fuel volumes is 0 to 100 liters but it is necessary that the fuel volume is 5 liters or greater. Alethic quantities are often provided in technical specifications.
Deontic quantities are concerned with obligation and permission. AS6969™ considers a ground vehicle traveling on a highway. While the speed capabilities of the vehicle are alethic quantities, the highway speed limit and the required speed to keep with traffic flow are deontic quantities.
Metrology addresses the epistemological concerns of values, i.e. how is the value of the measurand determined (the measurement procedure), what is the value uncertainty, and what is the value quantization. Measurement uncertainty is a statistical quantity that characterizes the dispersion of values that can be attributed to the measurement procedure. This may be expressed by a standard deviation or variance, or by the components of a covariance matrix. Where required, statistical quantities are provided in the coordinate reference system (CRS) tables of AS6969™.
A waveform quantity is a signal parameter that varies with time relative to a reference signal model. The model itself will define the parameters. For example, if a quantity varies sinusoidally, then the waveform quantities will be amplitude, frequency, and phase.
The purpose of AS6969™ is not to define the structure of how quantity modals are expressed in data models. It simply provides common terms that can be used for consistency across data models.