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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Problem statement</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Valentina Anita Carriero ID</string-name>
          <email>valentina.carriero3@unibo.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>University of Bologna</institution>
          ,
          <addr-line>Bologna</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2021</year>
      </pub-date>
      <abstract>
        <p>Understanding large ontologies, with diverse semantics and modelling practices, is still an issue, and has an impact on many ontology engineering tasks. While existing methods summarise ontologies by extracting the most important nodes or subgraphs, a complete overview of an ontology, and a comparison between multiple ontologies, are not supported. Based on the hypothesis that ontologies are designed as compositions of patterns, this paper presents a research proposal for developing a method able to extract conceptual components from multiple ontologies and the observed ontology design patterns implementing them.</p>
      </abstract>
      <kwd-group>
        <kwd>ontology design patterns</kwd>
        <kwd>ontology understanding</kwd>
        <kwd>empirical knowledge engineering</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>
        different modelling styles): e.g. the location component (being located at a place)
can be implemented in one or more ontologies as a binary (e.g. hasLocation) and
a n-ary relation (e.g. Location) between 3 arguments (Time, Object, Place), or
can be specialised as the location of a specific object (e.g. a building).
ODPs, being reusable template solutions to recurrent modelling problems [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ],
have been proposed as a tool for supporting ontology engineering and reuse:
however, they are often used unintentionally and, even if intentional, their use
is rarely made explicit e.g. through annotations [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. While contributing to the
development of ontologies on cultural heritage [
        <xref ref-type="bibr" rid="ref5 ref8">5, 8</xref>
        ], I experienced lack of tools
e.g. able to recommend candidate ODPs addressing a specific modelling
requirement. I also experienced the manual and time-consuming process of creating
well-documented ODPs [
        <xref ref-type="bibr" rid="ref4 ref7">4, 7</xref>
        ].
      </p>
      <p>Based on these premises, this research project aims at providing methods and
tools for supporting ontology understanding, and indirectly other ontology
engineering tasks, by (i) identifying modelling problems (CCs) common to
multiple ontologies and implemented with specific modelling solutions (ODPs), (ii)
analysing these solutions and comparing them with documented ODPs, (iii)
automatically annotating them to make them recognisable.
2</p>
    </sec>
    <sec id="sec-2">
      <title>Importance</title>
      <p>
        Automatically extracting CCs and their corresponding ODPs from KGs can
provide a basis for novel approaches to support ontology engineering tasks.
Ontology selection. An ontology designer may need to reuse existing
ontologies for modelling her data. The patterns implemented in an ontology reflect the
modelling problems that it addresses, rather than the collections of concepts it
contains. Therefore, a modularised, pattern-based and topic-centered description
of ontologies should support a better understanding, hence selection of them.
Ontology visualisation. Ontology visualisation is an important tool for
working with ontologies. Most of the existing frameworks show node-link views with
a focus on class hierarchies [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]. Large KGs limit the usability of these tools. The
patterns identified in KGs can be exploited for visualising a KG as a network of
conceptual components, making its inspection easier.
      </p>
      <p>
        ODP-based ontology engineering. Currently, ontology patterns are
developed manually and collected in repositories such as ODP Portal. Mostly based
on a top-down approach, these repositories unavoidably lack completeness [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ]
and do not provide information on the actual use of ODPs. Identifying ODPs in
KGs can provide actual examples of how catalogues’ ODPs are implemented in
ontologies, thus documenting their use, and can significantly enrich ODP
repositories with new patterns, emerged as a result of empirical analysis.
ODP-based ontology matching. Detecting ODPs implemented in multiple
KGs can help designers and ontology matching (OM) tools to generate
alignments between ontology fragments, i.e. groups of relations, thus contributing in
supporting pattern-based automatic OM procedures and KG linking.
3
      </p>
    </sec>
    <sec id="sec-3">
      <title>Related Work</title>
      <p>This research requires tackling different topics that have been investigated in
the literature.</p>
      <p>
        ODPs. Pattern-based ontology engineering methodologies, such as [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ], strongly
focus on ODP selection and reuse, but tool support for this task is still
insufficient, despite CoModIDE, a recent Protégé plugin for supporting pattern-based
design. To facilitate ODP reuse and documentation, [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ] proposes a simple
language for annotating ODPs in ontologies (OPLa). Although a richer and more
robust version of OPLa is desirable [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], it can provide a basis for automatic ODP
annotations in ontologies.
      </p>
      <p>
        ODPs detection. These methods focus on identifying parts of ontologies reusing
s-o-t-a ODPs. [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ] finds small evidences of ODP reuse in biomedical ontologies
starting from ODPs published in catalogues and tries to find their
implementations in ontologies, e.g. checking for import declarations and lexical similarities.
The limit of this top-down method is that it ignores emerging patterns.
ODPs discovery consists in exploring ontologies to find frequent repeating
structures. [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ] uses clustering techniques to detect syntactic regularities, i.e.
repetitive structures of axioms within an ontology. The result is a set of
axiom generalisations for each cluster, only limited to the logical description of
an ontology. [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ] proposes a tree-mining method to discover possible recurring
axiom patterns as frequent subtrees, where association analysis is used to mine
co-occurring axiom patterns, which may indicate emerging ODPs. This method
is unable to automatically assess whether a mined pattern is a fragment of a
known ODP, and does not take into account cyclic patterns and inferences.
Knowledge discovery aims to detect hidden patterns and regularities in large
datasets. [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ] proposes a method for automatically providing explanations to
data patterns using the background knowledge from the web: patterns at the
instance level could confirm patterns at the schema level, and background
knowledge could be used to explain such patterns.
      </p>
      <p>
        Ontology selection and understanding. Users can browse terms from
different ontologies on catalogues of ontologies (e.g. BioPortal) and semantic search
engines (e.g. Schemapedia). Comparison of ontologies and ODP-based filtering
of the results are not supported. Most ontology summarisation approaches [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]
look for the most important nodes or subgraphs using centrality measures: they
do not adopt an ODP-based approach and do not support comparison between
multiple ontologies.
      </p>
      <p>
        Ontology partitioning. Modularisation approaches (e.g. [
        <xref ref-type="bibr" rid="ref1 ref12">1, 12</xref>
        ]) split an
ontology in non-overlapping modules, that combined together form the original
ontology. They mainly focus on logical modularisation on one ontology at a
time, and no additional insight about the modules is provided.
      </p>
      <p>
        Complex ontology matching. Complex ontology alignments [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ] can
overcome the lack of expressiveness of simple (1:1) alignments. Different approaches
for complex OM have emerged in the literature; however, it is still regarded as a
challenge, and only alignments between two ontologies at a time are considered.
4
      </p>
    </sec>
    <sec id="sec-4">
      <title>Research questions</title>
      <p>My research project aims at addressing the following research questions, driven
by the respective hypotheses.</p>
      <p>RQ1: What are the Conceptual Components, and the ODPs implementing
them, used for modelling knowledge graphs on the web?
RQ1.1: Is the boundary of an ODP identifiable?
RQ1.2: How to assess that fragments from different ontologies address
the same modelling problem?
RQ2: Considering the ODPs observed on the web and the ODPs defined in
online catalogues of patterns: do they match?
RQ3: How to automatically annotate ODPs used in a KG?
(RQ1) H1: A combination of designated heuristics can support the
identification of the boundary of implemented ODPs
(RQ1) H2: Densely connected subgraphs detected in ontologies, grouped based
on the terminology used in the literal data describing their ontology
entities, may indicate modelling problems addressed by different
OWL implementations.
(RQ2) H1: Matching observed patterns with catalogues’ ones gives a measure
of how much, and how, predefined patterns are reused in practice.
(RQ3) H1: A designated language can annotate ODPs observed in KGs: their
components, attributes, relations.
5</p>
    </sec>
    <sec id="sec-5">
      <title>Method and Results achieved so far</title>
      <p>The intuition behind this research is that an ontology is (un)intentionally
developed as a composition of ontology design patterns, intended as modelling
solutions observed in existing ontologies, regardless their correctness or quality.
I hypothesise that these patterns can be empirically observed based on their
density and their vocabulary. I expect (i) the density of their internal
connections (i.e. connections between entities of the same ODP) to be higher than the
density of the connections between entities from different ODPs; (ii) the
combination of the words describing an ODP to evoke the relation it represents (e.g an
ODP implementing the location component may possibly include terms such as
place and is located at ). Community detection can recognise phenomena such as
(i), while text clustering allows me to exploit the vocabulary of ODPs in order
to group them based on their similarity, which may indicate they are addressing
the same modelling problem.</p>
      <p>CH ontologies corpus. As an empirical basis, I built a corpus of schemas
modelling Cultural Heritage (CH). The choice of selecting ontologies from this
domain is motivated by (i) my previous experience in developing CH
ontologies, and (ii) the general complexity of concepts and diversity of terminology
of this domain. Indeed, there are many different domains that are related to
the already vast domain of CH (e.g. geology for archaeological properties),
heterogeneous types of cultural heritage (musical, architectural, etc.), and different
cultural institutions have often their own classifications and terminologies. 43
ontologies have been selected from the literature, using a catalogue of general
purpose ontologies, i.e. LOV, and publishing an online survey.</p>
      <p>
        Method. For extracting CCs and ODPs from multiple ontologies, I adopt an
empirical approach that combines community detection, word sense
disambiguation, frame detection, clustering techniques (see Figure 1). The same method can
be exploited in order to group ODPs from actual ontologies and catalogues’ ones.
Intensional ontology graphs. In order to transform an ontology into a graph that
can be processed by community detection algorithms (undirected and unlabelled
graphs) while preserving the formalisation of the ontology conceptualisation, I
formally represent it as an intensional graph, i.e. a graph aiming at encoding
the intensional level of an ontology. An edge :p is generated between every two
nodes that are domain and range of a property :p. As for property restrictions on
classes, an edge :p links the class local to the restriction and the class in the
restriction expression. Finally, for each edge :p between two nodes :n1 and :n2, two
unlabelled edges are generated: the first between :n1 and a new node :n1-p-n2,
the second between :n1-p-n2 and :n2, in order to preserve the context of use of :p.
Community detection. Community detection splits networks into groups of nodes,
such that there is a higher density of edges within groups than between them:
since I expect the links between the entities involved in one ODP to be denser
than the links between entities from different ODPs, communities could
identify possible patterns. A modified version of a s-o-t-a algorithm [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ] is run on
the intensional graphs: the algorithm recursively splits communities with density
higher than the average density of all communities detected at the previous step,
since I experimented that this would improve the results. Starting from
communities as sets of nodes, the OWL ontology fragments containing these nodes
(classes and properties) are retrieved: for each node, I include the triples
asserting its type, domain and range axioms, inverse properties, super- and equivalent
classes, restrictions that involve at least one property within the community.
Clustering. If communities are possible ODPs, their vocabulary shall evoke the
relational meaning captured by these ODPs: if we cluster the communities
according to their vocabularies, we may identify conceptual components that are
shared by all of them, potentially. Each community is represented by a virtual
document : a string concatenating all English labels (or local IDs if no label
is present) from its entities, removing repetitions. These documents are
disambiguated with UKB and enriched with FrameNet frames1 (along with their more
general frames in the hierarchy) that have a close match with the synsets in the
virtual documents, by querying Framester. These virtual documents are given
as input to the K-Means clustering algorithm. Each cluster is labeled with the
most frequent frame(s) and/or synset(s) in the virtual documents belonging to
the cluster, and accompanied by a description, based on the concatenation of all
terms representing its communities.
      </p>
      <p>Based on this method, it is possible to build a catalogue of conceptual
components and observed ODPs, where each conceptual component links to its
associated ODPs within the ontologies: e.g. see the catalogue from the CH corpus.
Experiments. I run the method described in Method on both the CH corpus
and another corpus (Conf ) from the Conference evaluation track of the
Ontology Alignment Evaluation Initiative (OAEI). Through a manual inspection
of the communities, I found that there are recognisable patterns common to
many communities, which correlate with the modelling practice adopted for a
specific ontology (fragment). Some communities ( 5% of CH and 1% of Conf)
can be identified as missing a conceptual unity, because of poor axiomatisation
in the source ontology: e.g. communities grouping semantically heterogeneous
properties that are not involved in any restrictions. Instead, the majority of
the communities have a good level of semantic coherence e.g. representing the
acquisition of a cultural property from a previous owner, or the membership
in a conference. The clusters identified from both corpora represent different
conceptual components, at different levels of abstraction: components as event,
categorization, intentionally act are present in both corpora, while other
components specific to the domain emerge (e.g. performing arts in CH, award in
Conf). In both corpora, some clusters could be either split or merged.
Even if my goal is not to produce ontology alignments, I evaluated these initial
results against the ontology matching (OM) task, based on the hypothesis that,
given a pair of similar entities to be aligned, they should belong to either the
same cluster or two related clusters. The results of my method are compared
with alignments asserted within the ontologies of the corpus; alignments
generated by an OM tool with good performances; gold standard alignments on the
Conf corpus in the OAEI 2020 conference track. This experiment shows that
clusters and their relations may be used to improve the performance of
alignment algorithms, significantly reducing the dimension of the task.
1Abstract conceptualisations of objects or events that may be evoked by words.
Annotating ODPs. I am working on an extended version of OPLa annotation
language, able to annotate an ontology with its implemented ODPs and CCs.
6</p>
    </sec>
    <sec id="sec-6">
      <title>Evaluation</title>
      <p>The method will be evaluated on: (i) the communities as possible ontology design
patterns, (ii) the clusters of communities as possible conceptual components
(RQ1). The evaluation will be both manual and automatic. A first evaluation
of the initial experiments, consisting in manually inspecting communities and
clusters detected on the CH and Conf corpora and in analysing the results in
the context of the ontology matching task, has been already performed.
A corpus of ontologies annotated with the ODPs they implement will be built in
order to have a gold standard for comparing our automatically detected ODPs.
This activity will test if the extended annotation language is fit for the purpose
(RQ3). An experiment will be designed that clusters community from ontology
corpora and catalogues’ ODPs: based on the terminology, observed and s-o-t-a
ODPs addressing the same CC should end up in the same cluster (RQ2). The
results produced will go also through an evaluation phase by humans, in order
to empirically assess the degree of agreement between automatic and manual
detection of ontology patterns and conceptual components, possibly designing
crowdsourcing tasks. Even if a user-based evaluation of the catalogue would be
valuable, it is not an easy user study to be designed, as it would be evaluating key
concepts detection, since it requires involving experts in ontology design based
on patterns. Therefore, an indirect user-based evaluation will be considered, by
e.g.: (i) evaluating a pattern-based visualisation tool that will be based on my
method; (ii) using my method as a basis for ontology selection tasks.
These activities will be integrated within the EU H2020 project Polifonia, which
will realise an ecosystem of computational methods and tools for the European
musical heritage (MH) knowledge on the web: this will provide me with an
additional large-scale experimental basis.
7</p>
    </sec>
    <sec id="sec-7">
      <title>Discussion and Future Work</title>
      <p>Preliminary results of this research proposal are already satisfying and show the
potential of the method, but they still need to be improved.</p>
      <p>Future work will include different activities. The intensional graphs need to
include also all class expressions, in order to maximise the detection of relevant
communities and limit loss of information. A refinement of the conceptual
components (by merge or split of detected clusters) based on heuristics to be defined
will be a next step. I will study a method to match observed patterns, detected
in actual ontologies, to online catalogues’s patterns, which may have a great
impact for supporting interoperability. Moreover, the extended version of OPLa
will be necessary for automatically annotating ODPs in ontologies.
Acknowledgements. This research is conducted under the supervision of Dr.
Valentina Presutti and is supported by the CNR (E-RIHS infrastructure).</p>
    </sec>
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