The Semantic SI Ontology: Engineering, Alignment, and Validation of a

Semantic SI Model

Moritz Jordan

1 a

, Giacomo Lanza

1 b

, Shanna Sch

onhals

1 c

and S

oren Auer

2,3 d

Physikalisch-Technische Bundesanstalt (PTB), Braunschweig und Berlin, Germany

TIB - Leibniz Information Centre for Science and Technology, Hannover, Germany

L3S Research Center, Leibniz Universit

at Hannover (LUH), Germany

Keywords:

Ontology Engineering, Digital System of Units (D-SI), FAIR Data, Semantic Metrology.

Abstract:

The Semantic SI Ontology (SIS) provides a semantic model for representing the value of a physical quantity,

including kind of quantity, International System of Units (SI) measurement unit, and measurement uncer-

tainty, in accordance with the ofﬁcial Bureau International des Poid et Mesures (BIPM) recommendations.

Developed as a formal counterpart to the Digital System of Units XML schema deﬁnition (D-SI XSD), the on-

tology enables harmonized, machine-readable, and interoperable representation of metrological data. This pa-

per outlines the design rationale, the transformation methodology from eXtensible Markup Language (XML)

Schema to Web Ontology Language (OWL), and its alignment with existing semantic standards such as Quan-

tities, Units, Dimensions, and Data Types Ontologies (QUDT) and the SI Reference Point. Core ontology

structures - such as QuantityValue and MeasurementUncertainty - are discussed in detail. The paper also

presents the validation framework, including a Python toolchain for generating OWL individuals from XML,

Shapes Constraint Language (SHACL)-based shape validation, and reasoning with established OWL reason-

ers. Applications in ongoing projects, such as the Metadata4Ing and the Digital Calibration Certiﬁcate (DCC)

ontology, demonstrate the practical relevance of the SIS as a foundational component in the digital transfor-

mation of metrology.

1 INTRODUCTION

The International System of Units (SI) is a globally

recognized foundation for scientiﬁc measurements. It

is also the common foundation for numerous norms

and standards that are used in industrial applications

and ensure interoperability between various actors of

the global economic system. The Bureau Interna-

tional des Poids et Mesures (BIPM) provides and

maintains the ofﬁcial description of the SI in its of-

ﬁcial brochure (BIPM, 2024) which is one of the fun-

damental standards in metrology.

The SI brochure, in combination with the Interna-

tional Vocabulary of Metrology (VIM) (BIPM, 2012)

and the Guide to the Expression of Uncertainty in

Measurement (GUM) (JCGM et al., 2023), also pre-

scribes the correct way of reporting numerical infor-

https://orcid.org/0000-0003-0941-5950

https://orcid.org/0000-0002-2239-3955

https://orcid.org/0000-0002-0475-0568

https://orcid.org/0000-0002-0698-2864

mation, which includes: the numerical value, the kind

of quantity, the measurement unit and the measure-

ment uncertainty. In the context of digital transfor-

mation and Findable, Accessible, Interoperable, and

Reusable (FAIR) data principles, representing this

compound information in a machine-interpretable and

semantically rich format is an essential task, and cur-

rently one of the major challenges in metrology, as

recognized by the highest authority in metrology, the

Comit

e International des Poids et Mesures (CIPM), in

its Vision on Transforming the International System

of Units for a Digital World (CIPM, 2023).

In response to this need, the Semantic System of

Units Ontology (SIS) has been developed as a se-

mantic model that formalizes the representation of

quantity values, units, and measurement uncertain-

ties. This ontology provides a robust, logic-enabled

foundation for expressing metrological data in align-

ment with the BIPM recommendations. It is con-

ceived as the semantic complement to the Digital Sys-

tem of Units (D-SI) XML Schema Deﬁnition (XSD),

which has been widely adopted for structured digital

Jordan, M., Lanza, G., Schönhals, S. and Auer, S.

The Semantic SI Ontology: Engineering, Alignment, and Validation of a Semantic SI Model.

DOI: 10.5220/0013707600004000

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 17th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management (IC3K 2025) - Volume 2: KEOD and KMIS, pages

28-39

ISBN: 978-989-758-769-6; ISSN: 2184-3228

data exchange in the metrology community.

The SIS bridges the gap between eXtensible

Markup Language (XML)-based data serialization

and semantic modeling by leveraging the Web On-

tology Language (OWL). This enables both syntactic

validation and semantic reasoning over data involving

physical measurements. It allows digital systems to

interpret, validate, and interlink measurement data au-

tonomously—thus unlocking new potentials for auto-

mated compliance, intelligent calibration workﬂows,

and long-term traceability in smart manufacturing and

laboratory environments.

Moreover, the SIS has been designed to be mod-

ular, extensible, and interoperable with other promi-

nent semantic standards such as the Quantities, Units,

Dimensions, and Data Types Ontologies (QUDT) on-

tologies and the SI Reference Point (Miles et al.,

2022) from the BIPM. These synergies ensure that

SIS is not an isolated artifact, but a foundational se-

mantic infrastructure component compatible with in-

ternational efforts toward digital metrology.

This paper presents the rationale, design pro-

cess, and validation of the SIS. It elaborates on the

methodology of converting XML schema constructs

into OWL classes and properties, discusses align-

ment strategies with existing ontologies, and out-

lines the mechanisms for validating semantic integrity

via Shapes Constraint Language (SHACL) and au-

tomated reasoners. Finally, it highlights the ontol-

ogy’s application in real-world initiatives such as

Metadata4Ing and the Digital Calibration Certiﬁcate

(DCC), demonstrating its relevance and adaptability

in the digital transformation of metrology.

1.1 The ”SI Brochure” and Its Digital

Representations

The basic metrological knowledge, condensed from

150 years of research and international political

agreements, is curated and disseminated by the BIPM

in a collection of binding publications concerning de-

nomination, relationships and usability of metrolog-

ical terms and structures. Among these, the BIPM

brochure is the one which deals with measurement

units, namely regulating:

1. The International System of Units (SI), i. e. a list

of standardized units, rules for multiples and alge-

braic combination of these units, and deﬁnitions

for basic physical quantities.

2. Ofﬁcial recommendations for the use of the SI,

including prescriptions how to use quantities and

units (or their symbols) to report numerical val-

ues.

Other complementary recommendations are provided

by other BIPM publications, e.g. the denomination of

other fundamental metrological terms (VIM) and the

calculation and representation of measurement uncer-

tainties (GUM).

A plethora of digital representations for units ex-

ists, spacing from linear controlled vocabularies to

mature semantic models including logical and math-

ematical relations: a selection of such approaches is

reported in Section 2.2. Instead, a digital representa-

tion of the recommendations is still missing but it is

increasingly needed for automated reasoning, trace-

ability, and interoperability in scientiﬁc and industrial

contexts. This is the focus of the work described in

the present manuscript.

1.2 Previous Work: The D-SI XSD

The D-SI XSD, a comprehensive digital version of the

BIPM recommendations, was implemented within an

international cooperation in the context of DCC, in-

volving also partners from the industry. The result is

a metadata scheme for the structured representation of

quantity values, including constants of nature, serial-

ized in XSD. While machine-readable, it lacks seman-

tic richness and reasoning capability. This schema

served as the starting point for the SIS.

2 ONTOLOGIES IN

METROLOGY

2.1 Semantic Technologies in Metrology

The increasing digitalization of metrology, driven by

the need for automation, data interoperability, and

traceable digital records, has encouraged the adoption

of semantic technologies, which enable automated

data interpretation and information processing by ma-

chines. Semantic technologies - including ontologies,

Resource Description Framework (RDF), and reason-

ing tools - allow for the formal representation of do-

main knowledge in a machine-readable and logic-

enabled way. In metrology, this enables a standard-

ized and interoperable vocabulary for describing mea-

surement results, uncertainty declarations, measure-

ment units, measurement or calibration procedures,

and reference values.

Ontologies are particularly powerful for modeling

complex relationships among metrological concepts.

By making explicit the semantics of terms and data

structures, ontologies help bridge the gap between

disparate systems and organizations, improving ma-

The Semantic SI Ontology: Engineering, Alignment, and Validation of a Semantic SI Model

chine interpretability and reducing ambiguity in data

exchange.

2.2 Existing Ontologies Covering

Metrological Terms

Several ontology-driven efforts have emerged in re-

cent years to address semantic interoperability and

digital traceability in metrology and related domains:

• SI Digital Framework (BIPM)(Miles et al.,

2022):

This international initiative, coordinated by the

International Bureau of Weights and Measures

(BIPM), aims to create a semantic infrastruc-

ture for the SI in the digital age. One of its

key components is the SI Reference Point, a

machine-readable, RDF-based representation of

the SI Brochure. The SI Reference Point provides

canonical Uniform Resource Identiﬁer (URI)s for

SI units, preﬁxes, and constants and serves as a

trusted semantic reference for digital metrology

systems.

• The M-Layer (Hall, 2023):

This international initiative, coordinated by the

NCSLI consortium, aims to capture the semantic

complexity of quantities, introducing the concepts

of aspect (kind of quantity) and scale (ratio, inter-

val, ordinal, and nominal).

• QUDT (QUDT Working Group, 2023):

A general-purpose ontology widely used across

science and engineering. It includes a comprehen-

sive taxonomy of units and quantities, unit conver-

sions, and relationships between physical dimen-

sions. Although not ”metrology native”,it is well-

aligned with SI and has been adopted in several

industrial and research contexts.

• Ontology of Units of Measure (OM) (Rijgers-

berg et al., 2013):

A domain-neutral ontology for representing quan-

tities and measurement units. It provides reason-

ing support for unit compatibility and conversion,

and is often used in scientiﬁc computing and In-

ternet of Things (IoT) applications.

• Extensible Observation Ontology (OBOE)

(Madin et al., 2007):

Developed initially for ecological and environ-

mental research, OBOE models entities, observa-

tions, and measurements in a ﬂexible way. While

not designed speciﬁcally for SI-based metrology,

its conceptual structure overlaps with measure-

ment modeling and serves as an inspiration for

context-aware data models.

A somewhat longer collection of semantic de-

scriptions for metrological information, with a call for

their evaluation, is given in (Lanza et al., 2024), as

well in (Keil and Schindler, 2018).

2.3 Positioning the Semantic SI

Ontology (SIS)

The SIS distinguishes itself within this ecosystem as

a highly targeted semantic model for the precise, har-

monised, and safe digital representation of numerical

variables conforming to the SI and its related con-

cepts, such as constants, measurement uncertainties,

and quantity values. The SIS does not contain a vo-

cabulary or collection of quantities and units. Instead,

it is conceived as a data model deﬁning classes, prop-

erties, and validation rules to be used in operational

metrology in combination with such a collection, such

as QUDT, OM, or the more recent and authoritative SI

Reference Point. The SIS brings an additional seman-

tic layer, which guarantees, in addition, the machine

interpretability of data.

By providing a modular, extensible, and machine-

actionable model grounded in both formal ontolog-

ical principles and practical XSD implementations,

the SIS complements existing efforts and ﬁlls a cru-

cial niche in the semantic infrastructure for modern

metrology.

The SIS is available at the address https://www.

ptb.de/sis/ .

3 CREATING THE SIS

3.1 Methodology: Transforming

Schema Constructs into OWL

Constructs

The SIS was designed trying to build a simple but rig-

orous semantical representation of the BIPM recom-

mendations reported in the SI brochure, the VIM and

the GUM. By logically grouping all required ﬁelds

and considering the most relevant use cases occur-

ring in practice, we deﬁned the following groups of

classes:

• Classes expressing occurrences of a quantity: sin-

gle real value, single complex value, constant

value, real list, complex list, nested lists (Section

4.1)

• Classes expressing uncertainty declarations: uni-

variate/multivariate, standard/expanded, coverage

interval (Section 4.2).

KEOD 2025 - 17th International Conference on Knowledge Engineering and Ontology Development

Figure 1: Basic structure of the SIS ontology show-

ing the main parent classes sis:QuantityValue and

sis:MeasurementUncertainty, as well as the interac-

tions with the SI Reference Point (SIRP) and with QUDT.

The ﬁelds themselves were implemented either as

datatype properties, having as value elementary data

types (numeric, datetime, boolean, string) or as ob-

ject properties, having as value composite data struc-

tures (i. e. instances of classes). We adopted the D-

SI XSD as a blueprint for the choice of classes and

properties, using the mapping approach described by

(Wheeler et al., 2012). Some elements which were

too much serialization-speciﬁc or which could be ef-

fectively described with the help of restrictions were

left out in the mapping process.

In a subsequent step, a hierarchical structure

was established by introducing subclass relationships

where appropriate. In a further step, the concepts de-

ﬁned in the ontology were examined to deﬁne seman-

tic connections to existing domain frameworks, such

as the BIPM SI Digital Framework and QUDT, to en-

able reuse and ensure semantic interoperability.

3.2 Mapping of XSD Elements to

Ontology Constructs

Following the general rule observed by (Wheeler

et al., 2012), complex types were mapped to

owl:Class constructs. Simple types were trans-

formed into rdfs:Datatype to preserve their seman-

tic meaning, as they often reﬁne more general XSD

types through additional restrictions.

Globally deﬁned elements in the D-SI XSD -

such as six:Real, which is of type RealQuantity-

Type - were used to deﬁne the top-level concepts in

the ontology. The name of the global element (e.g.,

six:Real) was adopted as the ontology class name

(e.g., sis:Real), while the associated type (e.g. Re-

alQuantityType - see Figure 2) determined the struc-

ture of the class. Consequently, the elements de-

ﬁned within RealQuantityType were mapped to object

properties and datatype properties of the sis:Real

class (see Table 1 for an overview of the mapping of

types and elements).

Figure 2: RealQuantityType in the D-SI XML schema deﬁ-

nition.

Figure 3: Class of sis:CovarianceMatrix with ob-

ject property hasCovariance with range sis:Covariance

with positional information preserved by indices.

3.3 Design Decisions and Challenges

The development of the SIS, while grounded in a

well-deﬁned XSD, presented conceptual and techni-

cal challenges discussed in the following section.

3.3.1 Loss of Order from xs:sequence and

xs:list

One major limitation encountered during the schema-

to-ontology transformation process was the inability

of OWL (Web Ontology Language) to represent or-

dered sequences natively. The xs:sequence con-

struct in XSD implies a strict ordering of child ele-

ments - information that is semantically meaningful

in certain cases, such as:

• Ordered lists of values, such as numerical

datasets using xs:list.

• Covariance matrices, where both the order of

values and their multi-dimensional position are

critical.

OWL does not preserve element order in standard

property assertions. To address this, a dual strategy

was adopted:

The Semantic SI Ontology: Engineering, Alignment, and Validation of a Semantic SI Model

Table 1: Overview of the mapping of XML types to ontology constructs.

XSD XSD example Ontology Ontology example

complexType six:realQuantityType class sis:Real

simpleType six:unitPhaseType datatype ---

element with complexType six:covarianceMatrix object property sis:hasCovarianceMatrix

element with simpleType six:unit datatype property sis:hasUnitIdentifier

• In cases where ordering is not semantically im-

portant (e.g., sets of metadata properties or op-

tional nested values), the ordering information

was safely discarded during the transformation. If

the knowledge graph data is transformed to XML

data, the order information lies in the XSD.

• In cases where ordering is essential, a specialized

class pattern was introduced. These classes (e.g.

sis:RealInList or sis:Covariance) encapsu-

late:

– The actual numerical value (e.g., a matrix entry

or a real value in a list)

– One or more index properties (e.g.,

sis:hasRowIndex, sis:hasColumnIndex

or sis:hasListIndex) used to encode the

position of the value within the list or ma-

trix (see Figure 3 or sis:RealInList and

sis:ComplexInList in Figure 4 ).

This pattern preserves the full structure of ordered

collections in a way that is still compatible with OWL

reasoning and SPARQL Protocol and RDF Query

Language (SPARQL) querying, albeit at the cost of

some verbosity.

3.3.2 From Schema Typing to Semantic

Hierarchies

Another challenge was transitioning from a structural,

schema-driven typing system to a semantically mean-

ingful ontology class hierarchy. XML schema deﬁ-

nitions tend to emphasize data validation, using com-

plex types to group and constrain elements. However,

in ontological modeling, the focus shifts to conceptual

clarity and inheritance of meaning.

To this end, the mapping process required:

• Promoting XSD complex types to OWL classes.

• Introducing subclass relationships to reﬂect do-

main hierarchies not explicitly captured in the

schema.

• Reinterpreting simple types with value restric-

tions as RDF Schema (RDFS) datatypes, while

preserving their semantic constraints where pos-

sible.

This transition also required iterative domain val-

idation to ensure that the resulting ontology remained

faithful to both the formal structure of the XSD and

the conceptual integrity of metrological knowledge.

3.3.3 Ontology Size and Granularity

A further consideration was the level of granularity

for ontology classes and properties. The D-SI XSD

uses a rich variety of named simple types, many of

which are speciﬁc to particular use cases (e.g., dec-

imalType, intervalMinType). Rather than collapsing

these into overly generic types, the decision was made

to preserve semantic granularity in the ontology.

3.4 Ontology Governance

The governance of the SIS is closely aligned with

the underlying D-SI XSD, which serves as the pri-

mary source of truth for the ontology’s conceptual

scope. As such, the ontology will be updated to re-

ﬂect changes in the XSD, ensuring consistency across

both representations.

The next version of the D-SI XSD is being de-

veloped with an emphasis on long-term stability.

Once the ontology has reached full coverage of the

schema’s scope, it too is intended to become a stable

reference artefact. This stability is essential for en-

abling persistent identiﬁers, reproducible queries, and

interoperability across systems that consume or rea-

son over D-SI-based data.

Ongoing development, updates, and governance

of the ontology will be managed by a dedicated team

at the Physikalisch-Technische Bundesanstalt (PTB)

in Germany. This team will be responsible for cu-

rating changes, maintaining alignment with the D-SI

XSD, and ensuring the integrity and long-term sus-

tainability of the ontology. Requests for change, ex-

tensions, or clariﬁcations will be reviewed by this

team in coordination with stakeholders and domain

experts.

4 CORE STRUCTURE OF THE

SIS

The SIS (Jordan and Lanza, 2025) is designed to pro-

vide a precise, semantic representation of the con-

KEOD 2025 - 17th International Conference on Knowledge Engineering and Ontology Development

Figure 4: Hierarchy of sis:QuantityValue with the exemplary subclasses sis:Real sis:Complex and sis:Constant and

some of their properties (e.g. :hasValue, :hasUnitIdentifier).

cepts used in the D-SI XSD. Its core is built around

classes that represent quantities, constants, measure-

ment values, and their associated uncertainties. These

classes reﬂect the structure of the D-SI XSD, but

are extended and aligned with broader metrological

concepts through ontological modeling and alignment

with existing vocabularies such as the VIM (BIPM,

2012).

The SIS in its present state (Version v0.2.1) com-

prehends 29 classes, 17 object properties, 19 datatype

properties and 452 axioms.

4.1 QuantityValue: Central Abstraction

for Measured and Deﬁned Values

At the heart of the ontology is the abstract class

sis:QuantityValue, which serves as the superclass

for all types of numerical values and their associ-

ated units in the ontology. This includes both mea-

sured values (e.g., physical quantities) and deﬁned

constants.

sis:QuantityValue is deﬁned as semantically

close to the VIM concept of “quantity value” and

is annotated with a skos:closeMatch to the cor-

responding concept in the VIM thesaurus (BIPM,

2017). It serves as a structural and semantic anchor

for all types of value-bearing classes in the ontology.

The main subclasses of QuantityValue include:

• sis:Constant — A quantity with a ﬁxed value

(e.g., Planck constant), often used for deﬁned val-

ues in the SI.

• sis:Real — A scalar real-valued quantity.

• sis:RealList — A collection of real values

(e.g., for a data series).

• sis:Complex — A complex number with real

and imaginary parts.

• sis:ComplexList — A collection of complex

numbers.

Each subclass includes object and data properties

such as hasUnit, hasValue (see Figure 4).

4.2 MeasurementUncertainty:

Modeling Uncertainty in

Measurement

A second major branch of the ontology is

sis:MeasurementUncertainty, which repre-

sents uncertainty associated with quantity values.

This class generalizes different types of uncer-

tainty representations, from simple scalar standard

uncertainties to multivariate conﬁdence regions.

The class hierarchy under

sis:MeasurementUncertainty is structured as

follows (see Figure 5):

4.2.1 MeasurementUncertaintyUnivariate

This subclass represents one-dimensional (scalar) un-

certainties. It is further specialized into:

• sis:StandardMU — A standard uncertainty ex-

pressed as a standard deviation, u.

• sis:ExpandedMU — An expanded uncertainty

calculated by multiplying the standard deviation

by a coverage factor k > 1 to achieve a high cov-

erage probability P > 90%.

• sis:CoverageIntervalMU — An uncertainty

expressed in terms of a conﬁdence interval, also

associated with a coverage probability P > 90%.

These classes reﬂect common uncertainty expres-

sions found in calibration and conformity assessment

documents.

4.2.2 MeasurementUncertaintyMultivariate

This subclass represents uncertainties over multidi-

mensional quantities. It is further specialized into:

• sis:EllipsoidalRegion — A region deﬁned

by a covariance matrix and coverage probability,

typically modeled as an uncertainty ellipsoid.

• sis:RectangularRegion — A region deﬁned

by bounds on individual components, such as an

axis-aligned hyperrectangle.

The Semantic SI Ontology: Engineering, Alignment, and Validation of a Semantic SI Model

Figure 5: Hierarchy of sis:MeasurementUncertainty with its subclasses for univariate and multivariate uncertainties,

some ”grandchildren” classes and the relative datatype properties. The related classes for covariance matrices and covariance

elements are also shown. The classes are connected by the object properties :hasCovarIanceMatrix, :hasCovariance.

These multivariate structures are essential for

modeling correlations between components of vector-

valued quantities, such as force vectors or tensor

quantities.

4.2.3 ListMeasurementUncertaintyUnivariate

This class allows for the representation of lists of

scalar uncertainties, where each element may corre-

spond to one vector component. It is particularly use-

ful for representing uncertainty in lists of values. No-

tably, both StandardMU and ExpandedMU are mod-

eled as subclasses of this class as well, to support

cases where scalar uncertainties are expressed in a

list-like format.

4.3 Alignment and Reuse of Existing

Semantic Resources

One key principle in the design of the SIS is seman-

tic interoperability—the ability to integrate with and

leverage existing, widely accepted ontologies in the

metrology and quantity domain. Instead of develop-

ing an isolated model, the SIS reuses and aligns with

established vocabularies to enhance compatibility, re-

duce redundancy, and promote harmonization across

digital metrological resources.

4.3.1 Reuse of QuantityKind from QUDT and

SI Reference Point

The SIS introduces the class sis:QuantityType to

capture the conceptual dimension or kind of a phys-

ical quantity (e.g., length, energy, action). Rather

than creating an entirely new controlled vocabulary,

this class is mapped to and aligned with existing re-

sources, speciﬁcally:

• qudt:QuantityKind from the QUDT Ontolo-

gies;

• sirp:QuantityKind from the SI Reference

Point.

Instances of sis:QuantityType use OWL ob-

ject properties to reference external instances in these

ontologies. For example, an instance representing

the Planck constant may include an object property

sis:hasQuantityType linking it to qudt:Action,

an instance of qudt:QuantityKind (see Figure 6).

This alignment enables semantic clarity and facili-

tates interoperability in applications that already use

QUDT or SI RDF models.

4.3.2 Unit Representation and Semantic

Modeling of Compound Units

The SIS supports multiple approaches for encoding

units:

1. sis:hasUnit [Datatype Property] — This is a

string-based representation of a D-SI-compliant

unit, as it is being used in the D-SI XSD (e.g.

\joule\hertz\tothe{-1} for the unit of the

Planck Constant).

2. sis:hasSiMeasurementUnit [Object Property]

— This links a quantity to a structured semantic

representation of a unit, using the SI Reference

Point’s semantic model for units, including com-

pound units.

Compound units (e.g., joule per hertz) are mod-

eled using semantic decomposition into unit terms

realized in the SI Reference Point. An instance of

a compound unit, such as sirp:joule.hertz-1, is

composed of unit terms as seen in Figure 6. The SIS

reuses this model directly, enabling detailed reason-

ing over unit structures and consistency checks.

5 VALIDATION AND REASONING

Ensuring the correctness, consistency, and complete-

ness of the SIS is a key step toward its reliable use in

practical applications. This chapter describes the val-

idation and reasoning strategies used throughout the

KEOD 2025 - 17th International Conference on Knowledge Engineering and Ontology Development

Figure 6: Instance of Planck Constant.

ontology’s development process. The combination of

data-driven validation using existing XML data, con-

formance testing via SHACL shapes, and semantic

reasoning ensures that the SIS faithfully models the

underlying D-SI data model while maintaining logi-

cal rigor.

5.1 XML-to-OWL Conversion Tool

To support large-scale validation with existing

datasets, a custom Python tool was developed that

transforms D-SI XML data into OWL individuals

conforming to the SIS. This mapping algorithm sys-

tematically traverses XML instances that are valid ac-

cording to the D-SI XSD and generates a correspond-

ing RDF graph using OWL constructs.

By reusing real-world XML data as a source of

truth, this tool enables

• Rapid ontology validation against large data vol-

umes.

• Robust regression testing, ensuring that changes

to the ontology do not break compatibility with

existing XML data.

• Data-driven ontology population, facilitating

the bootstrapping of knowledge graphs from al-

ready validated sources.

The generated RDF individuals retain all seman-

tic information from the original XML representation,

including nested structures and datatype values, en-

abling end-to-end validation of the ontology’s model-

ing choices.

5.2 SHACL Shape Constraints

To enforce structural and semantic constraints at the

RDF level, SHACL shapes were written for each class

in the ontology. These shapes mirror the restrictions

imposed by the XSD, including:

• Cardinality restrictions on properties,

• Datatype and value ranges,

• Object property presence and relationships,

• Class hierarchies and expected typing.

For example, a SHACL shape for the class

sis:Real might ensure that it has exactly one

sis:hasValue property of type sis:decimal, a

sis:hasUnit property pointing to a recognized unit,

and an optional sis:hasStandardMU (standard mea-

surement uncertainty) property.

This dual modeling, with both OWL axioms and

SHACL constraints, allows the ontology to be seman-

tically expressive using OWL for reasoning and oper-

ationally veriﬁable using SHACL for structural con-

formance.

5.3 Validation Workﬂow and Graph

Comparison

A comprehensive validation workﬂow was estab-

lished to ensure that ontology instances generated

from XML data and those authored directly in Turtle

syntax are equivalent and conformant. The workﬂow

consists of the following steps (see also Figure 7):

1. Generation: D-SI XML ﬁles are transformed to

RDF/OWL individuals (in Turtle format) using

the Python mapping tool

The Semantic SI Ontology: Engineering, Alignment, and Validation of a Semantic SI Model

Figure 7: Validation workﬂow.

2. Import: Equivalent data authored directly in Tur-

tle format and XML-sourced data are loaded into

separate RDF graphs

3. Normalization: Both RDF graphs are serial-

ized into a canonical form using RDFLib (Team,

2025), a Python library for handling RDF graphs.

Blank node identiﬁers are standardized

4. Isomorphism Check: The two graphs are com-

pared for isomorphism, ensuring structural and

semantic equivalence across both representations

5. Logical Consistency: pySHACL also performs

OWL reasoning and checks for logical consis-

tency using built-in RDF/OWL reasoners.

6. SHACL Validation: The generated RDF graph

is validated against SHACL shapes using the

pySHACL Python library (Sommer, 2025).

This automated test suite is integrated into a

pytest-based testing environment, providing rapid

feedback during ontology development.

5.4 Advanced Reasoning with Prot

Beyond automated validation, further semantic rea-

soning is performed using the Prot

e ontology editor

with two OWL 2 reasoners:

• HermiT: For checking logical consistency, class

satisﬁability, and inferred subclass relationships.

• Pellet: For additional support of datatype reason-

ing and explanation of inferred axioms.

These tools help to uncover hidden inconsisten-

cies, unexpected inferences, and redundant axioms or

design ﬂaws.

Manual reasoning with Prot

e ensures that the

ontology behaves as intended under a standard OWL

2 DL reasoning regime, further enhancing the trust-

worthiness and robustness of the SIS.

5.5 Manual Validation with Domain

Experts

In addition to automated validation and reasoning,

manual review and feedback from domain experts

played a crucial role in ensuring the semantic accu-

racy and practical relevance of the SIS. Metrology

specialists were involved in iterative review cycles

throughout the ontology development process to as-

sess whether:

• The terminology and class structure reﬂected es-

tablished metrological concepts.

• Relationships between quantities, units, and un-

certainties were intuitive and aligned with real-

world usage.

• Key distinctions (e.g., between different types

of uncertainty or compound units) were properly

modeled and unambiguous.

• The ontology remained understandable and usable

for both human experts and machines.

These expert discussions led to several reﬁne-

ments, such as:

• Adjustments to class names to better reﬂect VIM

terminology.

• Inclusion of skos:closeMatch annotations to

clarify alignment with well-known deﬁnitions.

• Improvements to the handling of multivariate un-

certainties and unit representations.

This collaborative validation step ensured that the

SIS not only adheres to formal modeling standards but

is also aligned with the expectations and needs of the

metrology community.

6 APPLICATIONS OF THE SIS

The SIS was developed as a ﬂexible, interoperable se-

mantic data model for representing quantities, units,

KEOD 2025 - 17th International Conference on Knowledge Engineering and Ontology Development

and uncertainties in accordance with the SI. Since its

release, it has been the subject of discussions for its

integration in multiple metrology-related initiatives

and digital certiﬁcation frameworks. This chapter

presents current and emerging applications of the SIS.

6.1 Integration with Metadata4Ing

An ongoing discussion is underway with the Meta-

data for Engineering (M4I) workgroup within the Na-

tional Research Infrastructure for Engineering Sci-

ences (NFDI4Ing), which has created and maintained

the homonymous (M4I) metadata schema for the de-

scription of data, investigations and data generation

processes in the context of quantitative sciences, spe-

cially engineering and materials science. In future

versions of the M4I ontology (Arndt et al., 2022),

it is planned that numerical variables, which de-

scribe measurable quantities within engineering ex-

periments and simulations, will be modeled as sub-

classes of sis:QuantityValue.

By inheriting from sis:QuantityValue, M4I

will not need to deﬁne a separate uncertainty model.

The SIS’s inherent support for uncertainty (via the

MeasurementUncertainty class and its subclasses)

provides a robust and ﬂexible foundation for repre-

senting error bounds, coverage intervals, and multi-

variate uncertainty. This reuse avoids redundancy and

strengthens semantic alignment across domains, es-

pecially where scientiﬁc rigor and reproducibility are

essential.

This integration exempliﬁes the ontology’s abil-

ity to support broader scientiﬁc use cases beyond

classical metrology, enabling ﬁne-grained, semanti-

cally valid data annotations in digital research envi-

ronments.

6.2 Use in the Digital Calibration

Certiﬁcate (DCC) Ontology

Another major application of the SIS is its incorpo-

ration into the DCC Ontology, as described in (Jor-

dan et al., 2024). The DCC Ontology serves as a se-

mantic counterpart to the DCC XSD, which structures

data for digital calibration certiﬁcates compliant with

ISO/IEC 17025 — the international standard for the

competence of testing and calibration laboratories.

The transition from analog to digital calibra-

tion certiﬁcates represents a paradigm shift toward

machine-readable and machine-actionable metrologi-

cal data. This transformation is essential for reducing

manual processing effort, increasing accuracy, and

enabling full integration into digital quality manage-

ment systems.

The SIS is imported as the core model for quan-

tity values within the DCC Ontology. It provides stan-

dardized classes for physical constants, measured val-

ues, and associated uncertainty, all of which are re-

quired in calibration data. Notably, this semantic inte-

gration guarantees that every numerical value in a cer-

tiﬁcate is precisely annotated with its unit, uncertainty

model, and quantity type. Such clarity enables se-

mantic reasoning, automatic data validation, and dig-

ital audit trails, which will be necessary for quality

assurance and traceability in future digital metrology

workﬂows.

6.3 Use in the Digital Document

eXchange (DX) for ISO 170XX

Documents

A planned future application of the SIS is its inte-

gration into the DX Ontology (Jagieniak et al., tted),

which is being developed as a general semantic data

model for ISO 170XX standard-based documents.

These documents include but are not limited to:

• DCC

• Digital Calibration Request (DCR)

• Digital Test Report (DTC)

• Digital Reference Material Certiﬁcate

(DRMC)

The Digital document eXchange (DX) Ontology

provides a high-level, modular framework designed

to cover the semantic representation of various stan-

dardized digital documents used across the metrology

and quality infrastructure domains. For each docu-

ment type, the DX Ontology deﬁnes a dedicated sub-

model tailored to the speciﬁc structural and seman-

tic requirements of that document (e.g., a DCC sub-

model for calibration certiﬁcates, a DTC sub-model

for test reports, etc.).

While the SIS is not the core foundation of the

DX Ontology, it is a reusable component that will be

incorporated whenever quantity values need to be rep-

resented. This design promotes modularity and reuse,

enabling other parts of the DX Ontology to focus on

document-speciﬁc metadata, relationships, and pro-

cesses.

Especially in order to be used in industry appli-

cations and standardization documents, technology-

agnostic yet semantically precise description of the

metrological concepts described above are desper-

ately needed. One application example is the sub-

model description currently being created by the In-

dustrial Digital Twin Association (IDTA), a large in-

dustrial consortium deﬁning the standards for data ex-

The Semantic SI Ontology: Engineering, Alignment, and Validation of a Semantic SI Model

change in Industry 4.0, for Digital Quality Document

(Digital Calibration Certiﬁcate). Here, the description

of quantity values provided by SIS within the DCC

ontology can be directly used as described in section

6.2 and will facilitate the creation of these sub-models

(dig, 2025).

7 DISCUSSION AND

CONCLUSION

The development of the SIS represents a signiﬁcant

step toward harmonized, semantically rich represen-

tations of quantitative metrological data. By deriv-

ing the ontology from the established D-SI XSD,

we ensured compatibility with existing infrastructures

while leveraging OWL’s advantages for semantic ex-

pressiveness, reasoning, and data integration.

One of the key challenges addressed during de-

velopment was the translation of XML-speciﬁc con-

structs—such as element ordering and schema restric-

tions—into OWL, which does not natively support se-

quence semantics. Where necessary, alternative mod-

eling strategies were introduced, such as index-based

representations for ordered values like covariance ma-

trices. The reuse and alignment with existing on-

tologies, including QUDT, the SI Reference Point,

and VIM, further enhance the interoperability and

FAIRness of the ontology.

Validation was approached comprehensively,

combining automated tools (e.g., SHACL, RDF rea-

soning, isomorphism tests) with manual review by

metrology domain experts. This hybrid strategy en-

sures both technical correctness and domain ade-

quacy. Moreover, the Python-based tooling for con-

verting XML data into OWL individuals facilitates

large-scale testing and adoption.

A more in-depth analysis of how the SIS will be

performed when used for large-scale datasets as well

as within distributed systems which will be part of

the future work, e.g. when applied in the M4I com-

munity. The performance and scalability implications

that may come up with the broader use of SIS will

help to streamline and improve the ontology and con-

tribute to its further development.

The SIS has already demonstrated its applicabil-

ity in several contexts, including its upcoming inte-

gration into the DCC and M4I Ontology. Its design as

a reusable, domain-speciﬁc module for representing

quantity values with units and uncertainties makes it

an ideal building block for broader semantic infras-

tructures such as the DX Ontology, which aims to

support a wide range of ISO 170XX-compliant dig-

ital documents.

In conclusion, the SIS ﬁlls a critical gap in the se-

mantic metrology landscape by providing a machine-

interpretable, extensible, and interoperable model for

core SI-based data. Future work will focus on broader

adoption across metrological domains, further re-

ﬁnement through community feedback, and integra-

tion into national and international digital metrology

strategies.

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List of Abbreviations

BIPM Bureau International des Poids et Mesures. 1–

CIPM Comit

e International des Poids et Mesures. 1

D-SI Digital System of Units. 1, 2, 4–8, 11

DCC Digital Calibration Certiﬁcate. 2, 10, 11

DCR Digital Calibration Request. 10

DRMC Digital Reference Material Certiﬁcate. 10

DTC Digital Test Report. 10

DX Digital document eXchange. 10, 11

FAIR Findable, Accessible, Interoperable, and

Reusable. 1, 11

GUM Guide to the Expression of Uncertainty in

Measurement. 1, 2

IoT Internet of Things. 3

M4I Metadata for Engineering. 10, 11

NFDI4Ing National Research Infrastructure for En-

gineering Sciences. 10

OBOE Extensible Observation Ontology. 3

OM Ontology of Units of Measure. 3

OWL Web Ontology Language. 2–5, 7–9, 11

QUDT Quantities, Units, Dimensions, and Data

Types Ontologies. 2–4, 7, 11

RDF Resource Description Framework. 2, 7–9, 11

RDFS RDF Schema. 5

SHACL Shapes Constraint Language. 2, 8, 9, 11

SI International System of Units. 1–3, 7, 10, 11

SIS Semantic System of Units Ontology. 1–11

SPARQL SPARQL Protocol and RDF Query Lan-

guage. 5

URI Uniform Resource Identiﬁer. 3

VIM International Vocabulary of Metrology. 1, 2, 6,

9, 11

XML eXtensible Markup Language. 2, 5, 8, 9, 11

XSD XML Schema Deﬁnition. 1–8, 10, 11

The Semantic SI Ontology: Engineering, Alignment, and Validation of a Semantic SI Model