<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>Journal of the royal society
interface 3 (2006) 795-803.
[19] D. Garijo</journal-title>
      </journal-title-group>
      <issn pub-type="ppub">1613-0073</issn>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.3390/rs13122426</article-id>
      <title-group>
        <article-title>The landscape of ontologies in materials science and engineering: a survey and evaluation</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Ebrahim Norouzi</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Jörg Waitelonis</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Harald Sack</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Eggenstein-Leopoldshafen</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Germany</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Karlsruhe</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Germany</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>FIZ Karlsruhe - Leibniz-Institute for Information Infrastructure</institution>
          ,
          <addr-line>Hermann-von-Helmholtz-Platz 1, 76344</addr-line>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Karlsruhe Institute of Technology, Institute of Applied Informatics and Formal Description Methods</institution>
          ,
          <addr-line>Kaiserstrasse 89, 76133</addr-line>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Semantic Systems</institution>
          ,
          <addr-line>SEMANTiCS</addr-line>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2012</year>
      </pub-date>
      <volume>2941</volume>
      <fpage>166</fpage>
      <lpage>181</lpage>
      <abstract>
        <p>Ontologies are widely used in materials science to describe experiments, processes, material properties, and experimental and computational workflows. Numerous online platforms are available for accessing and sharing ontologies in Materials Science and Engineering (MSE). Additionally, several surveys of these ontologies have been conducted. However, these studies often lack comprehensive analysis and quality control metrics. This paper provides an overview of ontologies used in Materials Science and Engineering to assist domain experts in selecting the most suitable ontology for a given purpose. Sixty selected ontologies are analyzed and compared based on the requirements outlined in this paper. Statistical data on ontology reuse and key metrics are also presented. The evaluation results provide valuable insights into the strengths and weaknesses of the investigated MSE ontologies. This enables domain experts to select suitable ontologies and to incorporate relevant terms from existing resources.</p>
      </abstract>
      <kwd-group>
        <kwd>Knowledge representation</kwd>
        <kwd>Ontology evaluation</kwd>
        <kwd>Ontology reuse</kwd>
        <kwd>Materials informatics</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>ontology selection process.
CEUR</p>
      <p>ceur-ws.org</p>
    </sec>
    <sec id="sec-2">
      <title>1. Introduction</title>
      <p>Consequently, MSE domain experts struggle to identify and select suitable ontologies for their
applications. A comprehensive review encompassing all existing ontologies, detailing their reuse in the
MSE domain, and providing a quality assessment is urgently needed to guide expert decision-making.</p>
      <p>This paper aims to address the current lack of comprehensive knowledge about MSE ontologies
by providing a thorough review and analysis. Our objectives include identifying available ontologies,
understanding their specific purposes, developing criteria for ontology selection, and determining the
necessary information for informed decision-making by domain experts. All evaluation results are
available online4.</p>
      <p>The paper is structured as follows: Section 2 describes the methodology used to collect and evaluate
the MSE ontologies. Section 3 presents quantitative results of the review process and provides a thorough
discussion of these findings in the context of our study objectives. Finally, Section 4 summarizes the
primary outcomes of this study and outlines potential future research directions.</p>
    </sec>
    <sec id="sec-3">
      <title>2. Methodology</title>
      <p>This section outlines the comprehensive methodology employed to evaluate ontologies in the Materials
Science and Engineering (MSE) domain. The methodology comprises three Key components: expert
insights and surveys, quality requirements and corresponding criteria, and ontology evaluation metrics.
Each component significantly contributes to a thorough assessment of ontologies, empowering MSE
experts to select the most suitable ontology for their specific needs. The following subsections provide
detailed explanations of each methodological aspect:</p>
      <sec id="sec-3-1">
        <title>2.1. Expert Insights and Survey</title>
        <p>
          This subsection details the process of gathering expert insights and conducting a survey to identify
ontology requirements within the MSE domain. Expert insights provide a foundational understanding of
practical needs and challenges faced by domain professionals. To ensure the relevance and efectiveness
of the selected ontologies, an internal survey was conducted as part of the Platform Material Digital
(PMD) project5. The PMD project comprises 13 industry-led pilot projects with the shared requirement of
(re)using ontologies in the MSE domain. A key finding from our qualitative analysis is that the responses
of the 13 projects focused on diferent aspects of the ontologies. This highlights the varied priorities and
perspectives of the participating experts. The publicly available interview results6 highlight the specific
requirements identified by MSE experts. We asked the responsible PIs of the thirteen PMD projects to
gather essential information about MSE-related ontologies within their domain. The survey targeted
MSE experts, including material engineers, scientists, process and application engineers, and simulation
experts, aiming to standardize taxonomy and metadata for materials and their properties. Key survey
questions addressed the desired ontology domains, intended use and requirements of the ontology,
target users, and the specific competency questions (CQ) the ontology should answer. Table 1 presents
quality requirements, their justifications, and corresponding criteria, as determined by survey results.
The criteria mapped to these requirements include Completeness (ensuring suficient information
for specified tasks), Coverage (measuring the breadth of domain information), Availability (assessing
the accessibility of the ontology and its documentation), and Adaptability (evaluating the ontology’s
capacity to accommodate changes without compromising verified definitions). Relevancy measures the
ontology’s alignment to specified tasks, while Accuracy assesses the precision and correctness of its
representations. Compliance ensures adherence to defined rules and standards, and Internal Consistency
guarantees logical coherence. Credibility reflects the ontology’s acceptance and trustworthiness, and
Complexity measures its structural intricacy. Finally, Comprehensibility measures users’ understanding,
and Modularity assesses the ontology’s composability from discrete, manageable units [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ].
4https://ise-fizkarlsruhe.github.io/mseo.github.io/
5https://www.materialdigital.de/
6https://git.material-digital.de/ontologies/pmd-ontologies/-/tree/main/Partner%20project%20CQs
        </p>
        <p>
          This paper specifically focuses on Availability (presence of ontology files and documentation),
Adaptability (number of CQs answered correctly after changes), Complexity (structural properties like depth
and breadth), Internal Consistency (presence of logical/formal contradictions), Compliance (total
number of breached rules), Credibility (number of other ontologies that link to it or positive user feedback),
Comprehensibility (degree of annotations and naming conventions), and Modularity (number of
ontology partitions and root nodes). While the metrics for these criteria are defined, future work will
address Coverage, Completeness, and Accuracy for a more holistic evaluation [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ].
        </p>
      </sec>
      <sec id="sec-3-2">
        <title>2.2. Ontology Evaluation Metrics</title>
        <p>
          This subsection outlines the detailed metrics employed to evaluate the ontologies within the MSE
domain. Focusing on base, schema, and graph metrics, we measure ontology structure, complexity, and
usability. These metrics, categorized accordingly, were used in conjunction with the ROBOT tool7 [
          <xref ref-type="bibr" rid="ref5">5</xref>
          ]
and OntoMetrics8 [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ] to assess ontology quality.
        </p>
        <p>Table 2 presents the key metrics used in our evaluation including descriptions and significance. These
metrics align with W3C Semantic Web standards, specifically OWL and OWL DL. Base metrics include
Axioms, Class Count, Object Properties Count, Datatype Properties Count, Annotation Assertions
Count, and DL Expressivity. These metrics collectively indicate the overall size, complexity, and breadth
of the ontology, as well as the richness of relationships, data values, and applied logical constructs.
For schema metrics, Attribute Richness, Inheritance Richness, Relationship Richness, Axiom Class
Ratio, and Equivalence Ratio are included. These metrics reflect the detailed knowledge representation,
categorization, interconnectedness, logical definition detail, and redundancy among named classes.
Complex class definitions are excluded from these metrics. Graph metrics evaluated include Absolute
Root Cardinality (NoR), Absolute Leaf Cardinality (NoL), Number of External Classes (NoC), Depth,
Breadth, and Tangledness are evaluated. These metrics assess the foundational structure, granularity,
interdependence with external ontologies, hierarchical complexity, width, and interconnectivity of the
ontology.</p>
        <p>
          Furthermore, the OOPS! (Ontology Pitfall Scanner!) tool [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ] was to detect common ontology
development errors, including missing property domains or ranges, incorrect subclassing, and redundant
relationships. Identifying these pitfalls is crucial for ensuring ontology usability and efectiveness in
real-world applications. A detailed overview of the identified issues of MSE ontologies is provided in
the Appendix A.
        </p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>3. Results and Discussion</title>
      <sec id="sec-4-1">
        <title>3.1. Analysis of the MSE Ontologies</title>
        <p>In our comprehensive analysis of semantic artifacts relevant to the Materials Science and Engineering
(MSE) domain, a total of 94 semantic artifacts were identified, comprising 2 vocabularies and 92
ontologies. These ontologies can be categorized as follows: 11 general scientific ontologies, 7 without
publicly available files, 4 top-level ontologies, 8 mid-level ontologies, 60 domain-level ontologies, and
2 application-level ontologies. Notably, 7 ontologies could not be evaluated due to issues with their
imports. These ontologies include the Virtual Materials Marketplace (VIMMP) [83] Ontology, Chemical
Entities of Biological Interest (ChEBI) [84], Chemical Information Ontology (CHEMINF) [85], Metal
Alloy (MetalAlloy) [86], tribAIn Ontology [58], Semantic Materials Manufacturing Design (SEMMD)
[39], and Chemical Methods Ontology (CHMO) [31]. This highlights the necessity for improved import
handling and integration in ontology development processes. Consequently, 60 ontologies, as
summarized in Tables 3, 4, and 5, were evaluated using our introduced methodology9. This list comprehensively
details each ontology’s name, abbreviated short name, domain, projects utilizing it, purpose, publication
7http://robot.obolibrary.org/
8https://ontometrics.informatik.uni-rostock.de/ontologymetrics/
9Link to the list of ontologies</p>
        <p>Quality Requirements Justification Mapped Criteria
pdRroEemQhae1ni:nssiTvohefetmaoxanotnteorolimoalgysysccomiveuenrscitne.gprnoevciedsesaarycsoumb-- taThnhadetcttohevreemorna”tlcloonlomegcpyersseshhaoeryunlssdiuvbbee”-dcosoummgagpienlesstt.es eCroamgep,
lAevteanileasbsi,litCyov</p>
        <sec id="sec-4-1-1">
          <title>REQ2: The ontology should be capable of rep- The capability to represent various Completeness,</title>
          <p>resenting both experimental and simulation types of data indicates a complete and Adaptability,
Availdata. adaptable ontology. ability</p>
        </sec>
        <sec id="sec-4-1-2">
          <title>Accuracy is crucial for representing re</title>
        </sec>
        <sec id="sec-4-1-3">
          <title>REQ3: The ontology should accurately repre- lationships, and relevancy ensures that Accuracy, Relevancy,</title>
          <p>sent relations between diferent concepts. these relationships matter to the do- Availability
main.
wuRnEitiQhfy4e:xmiTsethtinaedgoasnttataondldoegasrycdrsmip.utisotnsstainndcaormdipzleiaanncde aSntadnidnatredrnizaaltcioonnsiismtepnlcieys. compliance
aCCbooimnlistpyislitaennccey,,IntAevrnaaill</p>
        </sec>
        <sec id="sec-4-1-4">
          <title>REQ5: The ontology must provide comprehen</title>
          <p>sive representations for experimental settings, Comprehensive representations imply Completeness,
Covoutcomes, high-throughput analysis data, and completeness and coverage. erage, Availability
literature.
wdRaEotQrat.h6:y aTnhdeveorniftioalbolgeyqumaulistyt mfaacnilaitgaetmeetnrutsotf- cTrreudsitbwiloirttyhainnedssacacnudravceyri.fiability imply ACvraedilaibbiilliittyy, Accuracy,
REQ7 (more specific): The ontology should Specificity for machine learning makes Relevancy,
Complexenable querying specifically designed for ma- it relevant, complex, and comprehen- ity,
Comprehensibilchine learning model development. sive for that purpose. ity, Availability
rRmeEsoQedne8tls(pm.reodriectsepdecviafilcu)e:sTfhroemonmtoalcohgiynemleuasrtnrienpg- apRnleedpterpenrseeesdnsitcaatnteiddoncporvooefpreamrgtaeiec.shiinmepllieeasrcnoinmg- eCroamgep,
lAevteanileasbsi,litCyoveaRnpEopQuli9gc:ahtfiooTrnhd.eivoernsteoplorgojyecstshboeuyldonbdeitsmporidmualaryr iMn oddivuelrasreitpyraonjedcttshiemapbliylitaydatoptbaebiulisteyd.
lAadriatpy,taAbvialiitlayb,iMlityoduof competency questions (CQs), licensing, last update date, homepage, ontology category, and a link to
the ontology file. Additionally, it includes references to academic papers, citation counts, practical use
cases, distinguishing features that contribute to its common use, and any special problems or challenges.</p>
          <p>Table 6 highlights the distribution of ontologies across various MSE sub-domains, with Materials
Representation and Materials Characterization having the most extensive coverage due to the complexity
of these fields. Process Modeling, Nanomaterials, Computational Materials Science, and Materials
Data also show significant ontology usage. However, domains such as Batteries, Chemistry, Energy
Systems, Tribology, Biomaterials, and Sensors comprise fewer ontologies, indicating a need for further
development to enhance their modeling capabilities and support advanced research applications.</p>
          <p>
            Among the ontologies identified, the top-level ontologies include: Basic Formal Ontology (BFO) [
            <xref ref-type="bibr" rid="ref8">8</xref>
            ],
Elementary Multiperspective Material Ontology (EMMO) [
            <xref ref-type="bibr" rid="ref9">9</xref>
            ], the Descriptive Ontology for Linguistic
and Cognitive Engineering (DOLCE) [11], and Suggested Upper Merged Ontology (SUMO) [10]. The
mid-level ontologies encompass PMD Core Ontology, Material Science and Engineering Ontology,
Baden Württemberg Material Digital Domain Mid Level Ontology, EMMO Datamodel ontology, EMMO
Mappings ontology, Materials Data Science Ontology, Ontology of Scientific Experiments, and The
Open Provenance Model for Workflows. The application-level ontologies are MatoLab Brinell Test
Ontology and Matolab Tensile Test Ontology.
          </p>
          <p>Our analysis highlights the diversity and complexity of MSE ontologies, reflecting their varied
applications and the necessity for rigorous evaluation methodologies. BFO is prominently reused in
16 ontologies, EMMO in 12, BWMD-MID in 3, NPO in 2, and SSN, PMD Core, and GPO in one each,
indicating its broad applicability and acceptance in the community. This frequent reuse suggests that
fTionteadl innutmhebeornotoflcolgays.ses de- isSmehnpotwlyasbwtrhiodeaedbrerarenadgdoetmhoafoincfoccnoocnvecepertapsgt.se
caonvdertehde.aHbiilgithyertocoreupnrteseTrottiaelsninumthbeeroonftoolbojgeyc.t prop- IaMnndodircebaeottebtsejertchrteepprvroeaspreieenrtttyiaetsoiofsnuregolgfaectsiootmnrsipchlheipexrsinibnteetterwarcceoteinonnnecscl.atsiosness.
pTorotaplerntiuemsibnetrhoefondtaotlaotgyyp.e aRHteitgfrlhiebceutrstcetosh.uenrtasnignediocfadteatdaevtaaliuleeds raespsorecsiaetnetdatwioitnhocflacslasesss.
iTnottahlenounmtobleorgoyf. annotations sSMthaoonrwdeasabntihlnietoyt.aamtioonusntenohfadnecsecrdiopctiuvmeemnetatatidoantaanpdrouvniddeedr-.
sTihveitydeosfcrtihpetioonntloolgoigcye.xpres- IsHnoidngiihcneagrt.eesxptrheessicvoitmy palleloxwitsyfoorf nluoagniccaeld caonndsctroumcptslexusreead-.
tArvibeurategse penrucmlasbse.r of at-
itHmioigpnhr,oeevrsisnveagnluutiesaaslbifniolidrtiyccoainntevaedpyepitnliacgialectdioomnksnp.olewxliendfgoermreaptrioesneanntadcAlvaesrsaegsepernculmasbse.r of sub-
taHinoednlpsastnriudnchutuinerdreaedrr.csHhtaiicngadhliesnrtgrvuahcloutuwersiknsnugog.wgelestdbgeetitsercacateteggoorirzizead</p>
        </sec>
        <sec id="sec-4-1-5">
          <title>Ratio of non-inheritance re- Important for understanding interconnectedness. Higher lationships to total relation- values imply a more interconnected and informative onships. tology.</title>
        </sec>
        <sec id="sec-4-1-6">
          <title>Average number of axioms Indicates the level of detail in logical definitions. Higher</title>
          <p>per class. ratios suggest more detailed and well-defined concepts.
aPxroiopmorsttioonallocflaesqseusiv.alence ttReherefmloesnctatsoreloredgdeyfu’isnnidendatneagcsryaetqaiuonindvaaslbeyinnlitto.ynH.yimghye,rivnadliuceastiinmgphroovwe</p>
        </sec>
        <sec id="sec-4-1-7">
          <title>Number of root classes in the ontology.</title>
        </sec>
        <sec id="sec-4-1-8">
          <title>Indicates cohesion and foundational structure. More root classes suggest a diversified foundational structure.</title>
        </sec>
        <sec id="sec-4-1-9">
          <title>Number of leaf classes in the ontology.</title>
        </sec>
        <sec id="sec-4-1-10">
          <title>Assesses granularity and detail. More leaf classes enhance the ability to capture fine-grained knowledge.</title>
        </sec>
        <sec id="sec-4-1-11">
          <title>Indicates the degree of interdependence with other on</title>
          <p>tologies. A higher count suggests better
interoperability, reusability, and alignment with external standards,
though it may also introduce complexity.</p>
        </sec>
        <sec id="sec-4-1-12">
          <title>Shows hierarchical complexity. Greater depth indicates more detailed hierarchical levels.</title>
        </sec>
        <sec id="sec-4-1-13">
          <title>Indicates the number of sibling classes, reflecting the ontology’s width. Greater breadth suggests comprehensive coverage at each level.</title>
        </sec>
        <sec id="sec-4-1-14">
          <title>Evaluates complexity and overlap in the hierarchical structure. Higher tangledness suggests greater complexity and potential dificulty in navigation.</title>
          <p>BFO and EMMO are considered high-quality foundational ontologies representing various aspects of
MSE.</p>
          <p>
            The study found that only nine of these ontologies explicitly published their competency questions:
PRovenance Information in MAterials science, Crystal Structure Ontology, Computational Material
Sample Ontology, Metadata4Ing Ontology, Open Energy Ontology, Materials Design Ontology,
Dislocation Ontology, SMART-Protocols, and PMD Core Ontology. Publishing CQs is crucial for clarifying
the ontology’s intent, facilitating adaptability assessment, and ensuring human-readable answers [
            <xref ref-type="bibr" rid="ref4">4</xref>
            ].
SENSEI, SmartProducts, SPITFIRE
          </p>
          <p>FP7, SemsorGrid4Env, Exalted,</p>
          <p>CSIRO
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Patterns (ODPs). The list was updated in June, and all the ontologies were found to the best of our knowledge.
7means that the information could not be found either from the ontology repository or from the publication
reference of the ontology.
While formulating CQs is an integral part of ontology development, they are often not published along
with ontologies, hindering evaluation eforts. Although modern design methodologies advocate for
user stories, personas, and contextual statements beyond CQs [87], none of the examined ontologies
adopted these approaches. This emphasizes the need for a more comprehensive approach to capturing
and addressing user needs and requirements.</p>
        </sec>
      </sec>
      <sec id="sec-4-2">
        <title>3.2. Evaluation of the MSE Ontologies</title>
        <p>The evaluation of MSE ontologies reveals varying levels of complexity and detail across diferent
sub-domains, as shown in Tables 9 and 10. In</p>
        <p>Materials Characterization, ontologies like EMMO
Crystallography and CIF-core demonstrate moderate axiom counts and high annotation axiom counts,
indicating a balance between detailed representation and descriptive metadata. CHAMEO, with
substantial object properties and annotation axioms, emphasizes detailed relationships and descriptive details.
CQs
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3</p>
        <p>Lic.
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CC0
1.0
CC BY</p>
        <p>4.0
CC BY</p>
        <p>4.0
CC BY</p>
        <p>3.0
In Process Modeling, GPO, EXPO, and PMDCO have high axiom and class counts, reflecting their
capability to model complex processes comprehensively. The high DL expressivity of GPO ( ℛ ℐ ( ) )
indicates its advanced logical constructs and reasoning capabilities.</p>
        <p>In Computational Materials Science, CMSO and MDO show diverse modeling approaches with
substantial axiom counts, indicating detailed and comprehensive domain representation. Materials
Representation ontologies like MatOnto and MSEO, with high axiom and class counts, suggest rich and
detailed modeling capabilities across various sub-domains. For Nanomaterials, NPO stands out with
extensive axioms and classes, indicative of detailed nanoparticle interaction modeling. eNanoMapper and
NanoMine, with lower axiom counts and simpler DL expressivity, focus on specific nanomaterial aspects.
In Mechanical Testing, MOL Brinell has a high axiom count but simpler DL expressivity ( ℒ ( ) ),
suggesting a thorough yet straightforward representation. Additive Manufacturing ontologies, such as
LPBFO, exhibit detailed and complex representations, whereas AMONTOLOGY ofers a broader but</p>
        <sec id="sec-4-2-1">
          <title>EMMO Crystallography, CIF Core Ontology, Dislocation Ontology,</title>
        </sec>
        <sec id="sec-4-2-2">
          <title>Characterisation Methodology Domain Ontology (CHAMEO), EMMO</title>
        </sec>
        <sec id="sec-4-2-3">
          <title>Microstructure, Material Science Lab Equipment Ontology, Chemical</title>
        </sec>
        <sec id="sec-4-2-4">
          <title>Methods Ontology, Crystal Structure Ontology, Point Defects Ontol</title>
          <p>ogy, Crystallographic Defect Core Ontology, Line Defect Ontology,</p>
        </sec>
        <sec id="sec-4-2-5">
          <title>Planar Defects Ontology, OIE Characterisation Methods</title>
        </sec>
        <sec id="sec-4-2-6">
          <title>EMMO General Process Ontology, PMD Core Ontology, SMART</title>
        </sec>
        <sec id="sec-4-2-7">
          <title>Protocols, Baden Württemberg Material Digital Domain Mid Level</title>
        </sec>
        <sec id="sec-4-2-8">
          <title>Ontology, Baden Württemberg Material Digital Domain Ontology, On</title>
          <p>tology of Scientific Experiments, Metadata4Ing Ontology, The Open</p>
        </sec>
        <sec id="sec-4-2-9">
          <title>Provenance Model for Workflows, Ontology to describe Workflows in</title>
        </sec>
        <sec id="sec-4-2-10">
          <title>Linked Data, Ontology for Simulation Modelling Optimization</title>
        </sec>
        <sec id="sec-4-2-11">
          <title>NanoParticle Ontology, eNanoMapper, MaterialsMine, NanoMine</title>
        </sec>
        <sec id="sec-4-2-12">
          <title>EMMO Atomistic and Electronic Modelling, Materials Design Ontology,</title>
        </sec>
        <sec id="sec-4-2-13">
          <title>Computational Material Sample Ontology, Dislocation Simulation and</title>
        </sec>
        <sec id="sec-4-2-14">
          <title>Model Ontology, Atomistic Simulation Methods Ontology, OIE models</title>
        </sec>
        <sec id="sec-4-2-15">
          <title>EMMO Datamodel ontology, EMMO Mappings ontology, MatWerk</title>
        </sec>
        <sec id="sec-4-2-16">
          <title>Ontology, Virtual Materials Marketplace (VIMMP) Ontology, OIE software</title>
        </sec>
        <sec id="sec-4-2-17">
          <title>EMMO Mechanical Testing, Matolab Tensile Test Ontology, MatoLab</title>
        </sec>
        <sec id="sec-4-2-18">
          <title>Brinell Test Ontology</title>
        </sec>
        <sec id="sec-4-2-19">
          <title>Additive Manufacturing Ontology, Laser Powder Bed Fusion Ontology,</title>
        </sec>
        <sec id="sec-4-2-20">
          <title>OIE manufacturing</title>
        </sec>
        <sec id="sec-4-2-21">
          <title>EMMO Battery Interface Ontology, EMMO Battery Value Chain Ontology Ontology</title>
        </sec>
        <sec id="sec-4-2-22">
          <title>Chemical Entities of Biological Interest, Chemical Information Ontology</title>
        </sec>
        <sec id="sec-4-2-23">
          <title>Smart Applications REFerence tribAIn Ontology</title>
        </sec>
        <sec id="sec-4-2-24">
          <title>The Devices, Experimental Scafolds and Biomaterials Ontology</title>
        </sec>
        <sec id="sec-4-2-25">
          <title>Semantic Sensor Network Ontology</title>
          <p>simpler structure. In the Batteries domain, EMMO BattINFO and EMMO BVC present similar metrics,
indicating detailed modeling capabilities.</p>
          <p>Schema metrics provide insights into the richness and interconnectedness of these ontologies, as
seen in Tables 11 and 12. High ACR and RR values denote detailed and interconnected models, which
are essential for capturing the complexity of material characterization. However, these also bring
increased computational challenges. High IR values suggest well-structured hierarchies, enhancing
knowledge organization but potentially complicating ontology maintenance. The diversity in metrics
indicates that while some ontologies are well-suited for detailed and complex modeling, others may
ofer more streamlined and eficient structures, highlighting the need for balance depending on specific
application requirements. For instance, in the Materials Characterization domain, ontologies like
CSO and PLDO show high Attribute Richness (AR) and Axiom Class Ratio (ACR), indicating detailed
knowledge representation and logical definitions, making them suitable for applications requiring
extensive detail. EMMO Crystallography and CSO excel in Inheritance Richness (IR), suggesting a
wellstructured hierarchical categorization, are beneficial for understanding domain taxonomy. CHAMEO
and DISO are notable for their high Relationship Richness (RR), implying a well-connected structure
that enhances relationship understanding. The choice of ontology depends on the application needs,
with CSO, PLDO, and CDCO recommended for detailed logical reasoning, EMMO Crystallography and
CSO for hierarchical structuring, and CHAMEO and DISO for comprehensive relationship mapping.</p>
          <p>Graph metrics, detailed in Tables 13 and 14, provide a deeper understanding of the structural properties
of the ontologies. Higher root cardinality (NoR) indicates a diversified foundational structure, enhancing
the ontology’s ability to cover a broad range of concepts. Conversely, a higher number of leaf classes
(NoL) suggests greater granularity and specificity, crucial for capturing detailed knowledge within the
domain. The number of External Classes (NoC) is calculated by comparing the ontology’s namespace
with the namespaces of the referenced classes. Classes that have a diferent namespace than those present
in the ontology are considered external. For ontologies that consist of multiple modules, the modules are
considered part of the core ontology. Therefore, classes from these modules are not treated as external.
To be classified as external, a class must have a namespace that difers from any of the namespaces used
within the core ontology and its modules. This ensures that only truly external references are counted,
reflecting the ontology’s degree of interdependence with other distinct ontologies. The number of
external classes (NoC) highlights the degree of interoperability and alignment with external standards,
with a higher count indicating better integration but potentially adding complexity. Together, these
metrics reveal the balance between foundational diversity, detail specificity, and interconnectivity,
impacting the ontology’s usability and efectiveness in representing complex domains. For instance,
in the Materials Characterization domain, ontologies like EMMO Crystallography and MSLE exhibit
high root cardinality, which may suggest a broad foundational structure. However, ontologies like
CSO and CDCO have fewer root classes, potentially indicating a narrower scope. It is important to
note that this metric is just a hint; a thorough examination of the ontologies’ content is necessary to
draw valid conclusions. An ontology with fewer root classes might still have a broader scope at deeper
levels of the hierarchy, and the reduced number of root classes could result from a higher-level top
classification. Ontologies such as EMMO Microstructure and OIE Characterisation Methods show high
leaf cardinality, reflecting a high level of detail and specificity. In terms of external class references,
CHAMEO and EMMO Microstructure demonstrate better interoperability with higher counts, whereas
PODO and PLDO have fewer external references, implying less reliance on external ontologies. Depth
and breadth metrics indicate complex hierarchical structures in ontologies like EMMO Crystallography,
while others, such as CSO and CDCO, display simpler, more focused structures. Overall, these metrics
highlight the diversity in foundational breadth, detail granularity, and external interconnectivity across
the Materials Characterization ontologies, impacting their comprehensiveness.</p>
          <p>For detailed evaluations in other domains, please refer to Appendix C and D. The appendix includes
the same evaluations applied to ontologies in diferent domains such as Biomaterials, Sensors, and
Energy, providing a comprehensive understanding of their complexities and structures.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>4. Conclusion and Outlook</title>
      <p>In conclusion, this study provides a comprehensive evaluation of 94 ontologies within the field of
Materials Science and Engineering (MSE), ofering a detailed analysis based on quality-control metrics.
The findings highlight both the strengths and weaknesses of the evaluated ontologies, emphasizing
their structural complexities, domain-specific relevance, and reuse of existing ontological frameworks.
However, the study also identifies critical areas for improvement, such as the limited adoption of
competency questions and ontology design patterns, and the need for better documentation and user
support to address common pitfalls and enhance overall quality and usability.</p>
      <p>Future work will focus on several key areas to further advance ontology development in MSE. Eforts
will be made to systematically identify and extract Ontology Design Patterns (ODPs) to enhance quality
and reusability. Additionally, further research will aim to comprehensively evaluate the
completeness, domain coverage, and accuracy of these ontologies by extracting relevant domain terms and
concepts within the subdomain of materials science. Moreover, the assessment of FAIRness (Findability,
Accessibility, Interoperability, and Reusability) of the ontologies will be incorporated into future studies.</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>The authors thank the German Federal Ministry of Education and Research (BMBF) for financial support
of the project Innovation-Platform MaterialDigital through project funding FKZ no: 13XP5094F (FIZ).
This publication was written by the NFDI consortium NFDI-MatWerk in the context of the work of
the association German National Research Data Infrastructure (NFDI) e.V.. NFDI is financed by the
Federal Republic of Germany and the 16 federal states and funded by the Federal Ministry of Education
and Research (BMBF) – funding code M532701 / the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) – project number 460247524.</p>
      <p>The authors would also like to acknowledge Sven Hertling for his valuable assistance in discussing
the reviews.
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    </sec>
    <sec id="sec-7">
      <title>Supplementary Information</title>
      <p>This supplementary section provides a comprehensive evaluation of various aspects of MSE ontologies.
Section A focuses on error detection using the OOPS! tool. Section B presents base metrics, examining
structural aspects. Section C evaluates schema metrics. Finally, Section D details graph metrics.</p>
    </sec>
    <sec id="sec-8">
      <title>A. Error Detection</title>
      <p>The OOPS! (Ontology Pitfall Scanner!) tool was employed for error-checking evaluations. Identifying
and categorizing these pitfalls is essential for the evaluation process. Critical pitfalls impact ontology
consistency, reasoning, and applicability, leading to significant issues in how the ontology is used and
interpreted. Important pitfalls, while not afecting the core functionality, can still degrade the quality
and reliability of the ontology. Minor pitfalls are less problematic but addressing them can enhance
the ontology’s organization and user-friendliness. By comparing the presence of these pitfalls across
diferent ontologies, MSE domain experts can make informed decisions about which ontology best
meets their needs, ensuring that the chosen ontology is robust, reliable, and suitable for their specific
applications. Table 7 describes only the pitfalls that exist in the MSE ontologies, along with their
descriptions and impact levels.</p>
      <p>Table 8 details the results of ontology evaluation using the OOPS! tool. Critical pitfalls afecting
ontology consistency and reasoning include P19 (Multiple domains or ranges for properties), P40
(Namespace hijacking), P31 (Incorrect use of owl:equivalentClass), P05 (Incorrect use of owl:inverseOf),
P29 (Incorrect use of owl:TransitiveProperty), and P27 (Incorrect use of owl:equivalentProperty).
Important pitfalls, although less severe, still afect ontology quality and should be addressed. Minor pitfalls,
while not critical, can be improved for better organization and user-friendliness.</p>
      <p>The frequent occurrence of critical pitfalls such as P19 and P40 across multiple ontologies suggests a
need for more stringent guidelines and validation tools during ontology development. The presence
of these pitfalls can significantly impact the usability and accuracy of the ontologies in real-world
applications. For instance, P19’s misinterpretation issues can lead to incorrect inferences, while P40 can
hinder efective data retrieval and integration.</p>
    </sec>
    <sec id="sec-9">
      <title>B. Base Metrics</title>
      <p>The Tables 9 and 10 provide an evaluation of the base metrics for MSE ontologies. It includes several
columns such as Domain, Ontology Name, and the total number of Axioms. Additionally, it details
the Class Count, Object Property (OP) Count, Data Property (DP) Count, and Annotation Axiom (Ann.
Axm.) Count. The table also highlights the Description Logic Expressivity10 (DL Expr.) and includes
information on the OWL2 profile 11.</p>
    </sec>
    <sec id="sec-10">
      <title>C. Schema Metrics</title>
      <p>Materials Characterization ontologies such as EMMO Crystallography (NoR: 33, NoL: 4) and MSLE (NoR:
63, NoL: 6) show broad foundational structures and detailed coverage, indicated by deep (Max Depth:
4) and broad (Max Breadth: 1760) hierarchies. CHAMEO and OIE Characterisation Methods have
high leaf cardinality (NoL: 34-35) and demonstrate good interoperability with moderate tangledness
(0.05-0.12). Process Modeling ontologies like GPO (NoR: 115, NoL: 8) and EXPO (NoL: 202) reflect broad
foundational coverage and significant depth (Max Depth: 8-12) with moderate tangledness (0.10-0.11).
PMDCO shows a balanced structure with extensive roots (NoR: 194) and low tangledness (0.02).</p>
      <p>In Computational Materials Science, ASMO (NoR: 28, NoL: 3) and CMSO (NoR: 31, NoL: 2) have broad
structures with no tangledness. DSIM (NoR: 17, NoL: 4) exhibits moderate depth and higher tangledness
10https://en.wikipedia.org/wiki/Description_logic
11https://www.w3.org/TR/owl2-profiles/</p>
      <p>Imp. Pitfall
l
a
c
i
t
i
r
C
t
n
a
t
r
o
p
m
I
r
o
n
i
M</p>
      <sec id="sec-10-1">
        <title>Description</title>
        <p>Multiple domains or ranges defined for
properties: Leads to misinterpretation as
a conjunction in OWL.</p>
        <p>Namespace hijacking: Terms from another
namespace are used without proper
definition, preventing information retrieval.</p>
        <p>Incorrect use of owl:equivalentClass:
Defining non-equivalent classes as
equivalent.</p>
        <p>Incorrect use of owl:inverseOf: Defining
non-inverse relationships as inverse.</p>
        <p>Incorrect use of owl:TransitiveProperty:
Defining non-transitive relationships as
transitive.</p>
        <p>Incorrect use of owl:equivalentProperty:
Defining non-equivalent properties as
equivalent.</p>
        <p>Lack of domain or range definitions:
Properties without defined domain or range
may cause misunderstandings.</p>
        <p>Defining classes as instances: Instances
incorrectly defined as classes, causing
confusion in class hierarchy.</p>
        <p>Misuse of transitive property: Improper
use of transitive property afects ontology
reasoning.</p>
        <p>Misuse of symmetric property: Misuse can
lead to incorrect inference.</p>
        <p>Using diferent naming conventions:
Inconsistent naming conventions reduce
ontology clarity.</p>
        <p>Use of deprecated classes or properties:
Use of deprecated elements afects
ontology maintenance.
(0.24). Materials Representation ontologies like MatOnto (NoR: 848, NoL: 13) and MSEO (NoR: 100,
NoL: 5) suggest deep, wide structures with no tangledness. Nanomaterials ontologies such as NPO
(NoR: 65, NoL: 5) and NanoMine (NoR: 1, NoL: 5) show extensive depth (Max Depth: 14) and breadth
(Max Breadth: 284-1593) with moderate to low tangledness (0.03-0.31). Mechanical Testing ontologies
like EMMO Mechanical Testing (NoR: 13, NoL: 7) and MOL Brinell (NoR: 17, NoL: 3) have moderate
depth (Max Depth: 3-7) and tangledness (0.21). Additive Manufacturing ontologies like AMONTOLOGY
(NoR: 5, NoL: 3) and LPBFO (NoR: 2, NoL: 4) show moderate depth and breadth with low tangledness.
Batteries ontologies like BattINFO (NoR: 10, NoL: 3) and EMMO BVC (NoR: 11, NoL: 4) suggest broad
foundational coverage with high horizontal coverage (Max Breadth: 1203-1781) and low tangledness
(0.01-0.05).</p>
      </sec>
    </sec>
    <sec id="sec-11">
      <title>D. Graph Metrics</title>
      <p>Materials Characterization ontologies like EMMO Crystallography (NoR: 33, NoL: 4) and MSLE (NoR:
63, NoL: 6) show extensive foundational structures and detailed coverage, with deep (Max Depth: 4)
and broad (Max Breadth: 1760) hierarchies. CHAMEO and OIE Characterisation Methods have high
leaf cardinality (NoL: 34-35) and good interoperability with moderate tangledness (0.05-0.12). Process
Modeling ontologies like GPO (NoR: 115, NoL: 8) and EXPO (NoL: 202) reflect broad foundational
coverage and significant depth (Max Depth: 8-12) with moderate tangledness (0.10-0.11). PMDCO
shows balanced structure with extensive roots (NoR: 194) and low tangledness (0.02).</p>
      <p>In Computational Materials Science, ASMO (NoR: 28, NoL: 3) and CMSO (NoR: 31, NoL: 2) indicate
broad structures with no tangledness. DSIM (NoR: 17, NoL: 4) has moderate depth and higher tangledness
(0.24). Materials Representation ontologies like MatOnto (NoR: 848, NoL: 13) and MSEO (NoR: 100,
NoL: 5) suggest deep, wide structures with no tangledness. Nanomaterials ontologies like NPO (NoR:
65, NoL: 5) and NanoMine (NoR: 1, NoL: 5) show extensive depth (Max Depth: 14) and breadth (Max
Breadth: 284-1593) with moderate to low tangledness (0.03-0.31). Mechanical Testing ontologies like
EMMO Mechanical Testing (NoR: 13, NoL: 7) and MOL Brinell (NoR: 17, NoL: 3) have moderate depth
(Max Depth: 3-7) and tangledness (0.21). Additive Manufacturing ontologies like AMONTOLOGY
(NoR: 5, NoL: 3) and LPBFO (NoR: 2, NoL: 4) show moderate depth and breadth with low tangledness.
Batteries ontologies like BattINFO (NoR: 10, NoL: 3) and EMMO BVC (NoR: 11, NoL: 4) suggest broad
foundational coverage with high horizontal coverage (Max Breadth: 1203-1781) and low tangledness
(0.01-0.05).
Additive
Manufacturing
Batteries
Biomaterials
Sensor
Energy</p>
      <p>NoC</p>
    </sec>
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