Metrology Vocabulary

This vocabulary was originally based on VIM3 (see https://jcgm.bipm.org/vim/en/info.html); however, the VIM3 distinction between quantity [VIM3: 1.1] and kind-of-quantity [VIM3: 1.2] led to using Prof. Rene Dybkaer's seminal work, An ontology on property, as a source of guidance for formalizing a VIM3-like vocabulary of metrology for quantities and units.

The VIM4 Committee Draft of January 11, 2021 constitutes a welcome improvement in the precision and meaning of the vocabulary, that, together with related JCGM documents explaining the significant changes from VIM3 to VIM4 greatly facilitated formalizing VIM4 as an ontology. This formalized vocabulary is made publicly available with the objective of providing additional input to the upcoming 25th meeting of the JCGM scheduled for 05 December 2022 with respect to publication options considered for VIM4 (see 'Development Line 2: adding machine readability' in Report from WG2 JCGM/2020-07).

The following diagrams summarize the formalization of VIM4

Taxonomy of properties

VIM4.1-properties

Quantities, Units and Values

VIM4.1-general,individual,units,values

Systems of Quantities and Units

VIM4.1-systems

Note that this representation supports multiple SystemsOfQuantities and SystemsOfUnits. The formalization ensures that the following turtle pattern must be consistent for all tuples of SQ, SU, Q, M:

SQ a vim4:SystemOfQuantities ; vim4:systemHasUnitaryQuantity Q .
SU a vim4:SystemOfUnits ; vim4:given SQ ; vim4:systemHasUnit M .
M vim4:instantiates Q .

Measurement Units

VIM4.1-units

Scales

VIM4.1-scales

Measurement

VIM4.2-Measurement

OWL2-DL Unit Consistency Checking

VIM4.1-unit consistency

The formalization ensures that any UnitaryQuantityValue must be consistent in the sense that the following paths must lead to pairs of GeneralUnitaryQuantity, (uq, aq), defined as follows:

• uq is any GeneralUnitaryQuantity reachable via the following SPARQL expression: unit.isMultipleOf*.instantiates

• aq is the GeneralUnitaryQuantity reachable via the following SPARQL expression: isAttributedTo.instantiates

Then for each such pair, one of uq.specializes* must be the same as aq.

Dimensional Analysis

Dimensional analysis is a procedure for determining what VIM4CD: 1.7 quantity dimension defines as the:

relation of a quantity to the base quantities of a system of quantities as a product of powers of factors corresponding to the base quantities, omitting any numerical factor

This analysis requires closed-world knowledge of the following:

• Instances of SystemOfQuantities (VIM4CD: 1.6)

• For each such system:

  • Instances of GeneralUnitaryQuantity that are its VIM4CD: 1.4 base quantities
  • Instances of GeneralUnitaryQuantity that are its VIM4CD: 1.5 derived quantities Each derivation in turn requires information about the derivation factors w.r.t other GeneralUnitaryQuantities

Formalizing this analysis in SPARQL 1.1 Query and Update should be possible in principle, see src/sparql/dimensional-analysis for such an attempt.

The strategy involves the following induction principle:

0. The initial step involves the special case of a base quantity, bq, for which the dimension is trivially 1 for bq and 0 for all other base quantities.
1. Find a derived quantity, dq, whose factors involve quantities with known dimensions. Calculate the dimension of dq` by raising the dimension of each dependency according to the corresponding factor and simplifying the resulting product of dimension factors.
2. Repeat step (1) until all derived quantities have been processed.

Trying to implement this strategy with SPARQL 1.1 queries and updates resulted in a few practical problems using Apache Jena 4.3.2 (see: https://jena.apache.org/download/index.cgi):

1. According to the SPARQL 1.1 Update, an update operation results in either success or failure. However, the specification does not stipulate the exact form of such a result. This makes it difficult to verify whether a particular update produced the desired triples.

For example, the update corresponding to step 0 is here:

0-base-quantity-dimension.sparql

When submitting this update to Jena Fuseki, the server responds simply: Update succeeded.

Fortunately, one can easily confirm the update indeed worked with the following query: quantity-dimensions.sparql

For step 1, the following update was intended to handle the case of derived quantities that depend on a single quantity with a dimension: 1-derived-quantity-dimension.sparql

When submitting this update to Jena Fuseki, the server responds simply: Update succeeded.

However, performing the query again shows that no new triples were inserted! Changing the update to a query (see the commented select statement) produces tuples that confirm the where clause is working properly. It is unclear why the insert for the same where clause does not actually insert these tuples.

2. Even if sparql query/update had worked, this approach for formalizing an inductive algorithm is very awkward.

To encode the closed-world semantics of this analysis in SPARQL, it is necessary to use non-trivial filter clauses to ensure that the where clause checks for all relevant cases.

This exercise warrants looking for a different strategy to implement dimensional analysis.

In the case of

Important note about this repository

This repository depends on the branch trig-format of this fork: https://github.com/NicolasRouquette/core-vocabularies until this PR is merged: opencaesar/core-vocabularies#26

The build.gradle is configured to resolve the core-vocabularies from https://jitpack.io/#NicolasRouquette/core-vocabularies/