32.2. VIM 4 2CD — International Vocabulary of Metrology
Indexed by VIM 4 2CD clause. The 2CD is a restricted committee draft; only clause numbers and terms are recorded.
The correspondence is mostly with this work's core spine — VIM's quantity,
ratio/interval/ordinal quantity, measurement scale, value of a quantity,
and the measurement principle/method/procedure chain map directly to PKC
declarations. Three VIM concepts reach into the further layers: quantity
dimension (1.9) and quantity with the unit one (1.10) are the Dimension
layer's dim map and the dimension-one thesis; quantity calculus (1.29) is the
Interaction algebra; the international system of quantities (1.8) is the
ISO/IEC 80000 catalogue and the coherent derived unit (1.15) the unit each
catalogued kind carries.
JCGM, International Vocabulary of Metrology — Basic and general concepts and associated terms (VIM), 4th edition, Committee Draft 2, 2023-07-31
| Locus | Term | This work | Note |
|---|---|---|---|
| 1.1 | quantity | Quantity | |
| 1.2 | quantities of the same kind | MutuallyComparable | |
| 1.3 | ratio quantity | IsRational | |
| 1.4 | interval quantity | IsDifferential | |
| 1.8 | international system of quantities (ISQ) | catalogue | the ISO/IEC 80000 catalogue of quantity-kinds |
| 1.9 | quantity dimension | toDimension | the forgetful dim map into PhysLib |
| 1.10 | quantity with the unit one | dim_not_injective | the dimension-1 thesis: distinct kinds collapse to one dimension |
| 1.12 | measurement unit | MetrologicalUnit | |
| 1.15 | coherent derived unit | CataloguedKind | the coherentUnit of each kind |
| 1.20–1.21 | multiple / submultiple of a unit | SIPrefix | the decimal prefix factor |
| 1.23 | measurement scale | ValueScale | |
| 1.24 | value of a quantity | PropertyValue | |
| 1.29 | quantity calculus | KMul | kind interaction (KMul / KDiv) |
| 1.30 | quantity equation | ProductKind | realized as R12 kind-laws |
| 1.33 | ordinal quantity | IsOrdinal | |
| 2.4 | measurement principle | ExaminationPrinciple | |
| 2.5 | measurement method | ExaminationMethod | |
| 2.7 | measurement procedure | ExaminationProcedure | |
| 2.12 | measurement model | Relation | the mathematical relation among the quantities involved, attached to a declared boundary as a checked theorem edge |
| 2.13 | measurement function | RelationKind | "f may symbolize an algorithm" — the four ways an implementing function may relate to its model: equals, inverts, refines, bounded by |
Many VIM clauses have no PKC counterpart, for two reasons. Some are metrological-
procedure concerns outside this ontology's scope — true value (1.26),
conventional value (1.27), measurement result (2.10), measured value (2.11),
measurement model/function (2.12–2.13), influence quantity (2.16),
correction (2.17), and the metrology/measurand/primary method terms (2.2,
2.3, 2.6, 2.8, 2.9). Others are not yet formalized: the base/derived
quantity and base/derived/off-system unit distinctions (1.6, 1.7,
1.13, 1.14, 1.18), system of quantities/of units as first-class objects
(1.5, 1.16, 1.17, 1.19), reference quantity (1.11), and the
unit/numerical-value equation forms (1.31, 1.32). The §1.22 conversion factor
between units is, by contrast, now formalized — carried as a power-of-ten exponent
(conversionExponent), with the conversion round-trip proved exactly over \mathbb{Z}
and numerically over \mathbb{R} (requirement R17).