Summary of discussion

1. Introduction

This document attempts to summarise part of the discussion so far. Very interesting threads about:

• the relationships between quantities and measurement methods;
• non-scalar quantities;
• dimensionless quantities, especially angle;

have not yet been addressed.

Sources

The principal sources of this document have been:

• the International Vocabulary of Metrology — Basic and General Concepts and Associated Terms (VIM) (http://www.bipm.org/en/publications/guides/vim.html);
• a UML model derived from VIM, with an extension for scales, developed by a team including NIST, which was supplied by Ed Barkmeyer;
• content of the e-mail discussion on [uom-ontology-std].

2. A strawman for quantity

A strawman UML diagram for "quantity" is shown in Figure 1:

Figure 1: Strawman for quantity

The differences between the Strawman and the original UML diagram supplied by Ed, include the following:

• The concept "quantity" has been split into generic quantity and particular quantity.
• The concept magnitude of quantity has been introduced.
• A quantity value does not necessarily reference a unit. This is not what the VIM says. There are a number of things which could be referenced, including a unit.
• The concept particular phenomenon body or substance has been introduced. This seems appropriate because quantities do not exist without something to possess them.

The UML diagram does not purport to be an ontology, but is an informal representation of the concepts related to "quantity" that have been discussed so far and their relationships.

The text associated with the UML objects shows an unsolved problem, as follows:

• Rockwell C hardness (150 kg) is shown as an example of generic quantity. It seems appropriate to include Rockwell C hardness (150 kg) as a generic quantity alongside thickness or radius, because it is something that can be measured for a particular solid object.
• Rockwell C hardness (150 kg) is shown as an example of kind of quantity. It seems appropriate to include Rockwell C hardness (150 kg) as a kind of quantity alongside length, because a measurement of Rockwell C hardness (150 kg) provides an expression of a magnitude of quantity that is within Rockwell C hardness (150 kg). Similarly a measurement of radius provides an expression of a magnitude of quantity that is within length.

The same would be true of mass.

3. A strawman for system of quantities

A strawman UML diagram for systems of quantities is shown in Figure 2:

Figure 2: Strawman for system of quantities

It was pointed out during the discussion that:

• there can be many different systems of quantities, with different base and derived quantities;
• a system of quantities is not the same as a system of units.

Both conclusions are also contained within the VIM. Hence being a base quantity or derived quantity is not a inherent property of a kind of quantity, but a relationship between a kind of quantity and a system of quantities.

4. A strawman for system of units

The text in the VIM says that a base unit or derived unit for a system of units correspond to a base quantity or derived quantity respectively. The VIM does not say that there is anything special in the way in which a unit is defined that makes it a base unit or derived unit.

A strawman UML diagram for system of units that is analogous to the diagram for system of quantities is shown in Figure 3:

Figure 3: Strawman for system of units

The original UML diagram supplied by Ed contains the text definition "A base unit is defined by a physical phenomenon, i.e., a 'definite description'". Following this approach it is natural to make base unit a subclass of measurement unit. However an "off-system measurement unit" may also be defined by a physical phenomenon. Hence it may be best to add this as shown in Figure 4.

Figure 4: Strawman distinguishing units defined by a physical phenomenon

5. A strawman for scales

The discussion so far has recognised the importance of scales, but has not gone into details. Extracting from the original UML diagram for scales supplied by Ed, and using VIM terminology wherever possible, a strawman UML diagram is shown in Figure 5.

Figure 5: Strawman for scale

The object space of values has been added. For most scales, this is a real or integer interval, perhaps unbounded. However, it could be something else, such as a sequence of letters "a", "b", "c", etc..

VIM does not give an example of conventional reference scale. Perhaps ITS90 is such a scale.

The relationship between scales and units has not been addressed in this strawman.