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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Ontological Patterns for Modeling the Validity of Spatiotemporal Statements</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Nicola Carboni</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>University of Geneva</institution>
          ,
          <addr-line>1, Rue De-Candolle 1205 Geneva</addr-line>
          ,
          <country country="CH">Switzerland</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>The paper tackles the challenges of modeling the temporal validity of artist-recorded locations documented in exhibition catalogs by proposing three diferent ontological patterns for recording spatiotemporal-constrained assertions in a Knowledge Graph. Exhibition catalogs often document the address used by an artist participating in exhibitions. The analysis of this information ofers significant insights into the spatial and social dimensions of artistic communities. However, the time-bound nature of the information makes its modeling particularly challenging, as it requires a framework that can efectively represent both the spatial and temporal dimensions of the relation. The connection between artist and their address, in fact, is always a fluent, a relationships that only hold within specific time intervals. To overcome this challenge, the study proposes and compares three ontological patterns designed for formalizing the dynamic aspects of spatial, temporal, and conceptual characteristics of an entity. The three approaches, based on RDF-star, CIDOC-CRM, and 4D ontology, are evaluated based on their ability to accurately represent the diachronic nature of addresses, formalizing (whether implicitly or explicitly) the validity of spatiotemporal assertions, and facilitating data integration and analysis.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Ontological Patterns</kwd>
        <kwd>Knowledge Graphs</kwd>
        <kwd>CIDOC-CRM</kwd>
        <kwd>Fluents</kwd>
        <kwd>Spacetime</kwd>
        <kwd>Temporal Validity</kwd>
        <kwd>Digital Humanities</kwd>
        <kwd>Digital History</kwd>
        <kwd>Digital Art History</kwd>
        <kwd>Cultural Heritage</kwd>
        <kwd>Exhibition Data</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        With the increasing availability of digital museum resources researchers can now potentially explore
the circulation of art and artists across the globe. Catalogues raisonnés and exhibition catalogs provide
crucial information on what has been produced by an artist as well as where and when it was exhibited.
Studying exhibitions means examining the history of forms through the circulation of ideas, images,
and artworks. They are a primary medium for the construction [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ] and reinforcement [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ] of the artistic
canon. Datafication of exhibition information opens the door to the use of novel methodologies (e.g.,
distant reading) to investigate the phenomenon at scale, specifically in relation to important topics such
as the geography of art, or the development of the artistic communities. For such a study to take place,
however, it is important to integrate multiple datasets, which still present some ontological challenges,
specifically with respect to the modeling of the temporal and spatial dimensions. Interconnecting
scattered collections through a shared conceptualization is, therefore, a matter of urgency, specifically
given the rise of data-driven studies in fields such as Digital Art History and Cultural Analytics [
        <xref ref-type="bibr" rid="ref3 ref4">3, 4</xref>
        ].
      </p>
      <p>This paper tackles the challenge of accurately modeling the temporal validity of artist locations
recorded in exhibition catalogs, where multiple addresses for the same artist are often documented
over time. Analyzing this data can reveal the extent to which the lives of these artists were
interconnected, ofering insights into the social and urban dimensions of the community. However, it also
raises the question of how to model the temporal validity of spatial and diachronic information, such
as an address. This paper seeks to answer this question by developing ontological patterns that can
efectively model the temporal validity of artist-recorded addresses in a way that supports both
detailed historical analysis and large-scale data integration. To develop the answer, the contribution
begins with an initial literature review (section 2), followed by an examination of the use case and its
information requirements (section 3, 4). Section 5 then presents three potential ontological patterns
for modeling the temporal validity of address. Section 5.2 examines how RDF-star can help express
the temporal validity of rdf statements. Section 5.3 introduces a CIDOC-CRM spatiotemporal pattern
(3D+1 modeling) for bounding the documentation of spatial features in time. Section 5.4 presents a
pattern that instantiates each historical trace of the address as a distinct spatiotemporal region (4D
modeling). An analysis of the advantages/disadvantages of these patterns is provided in section 6.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <p>
        The annotation of temporal dimensions in RDF has been extensively studied. A recent survey [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]
ofers a comprehensive review. A series of articles have been published on the use of CIDOC-CRM,
and its extension CRMgeo, for recording spatial regions [
        <xref ref-type="bibr" rid="ref6 ref7 ref8 ref9">6, 7, 8, 9</xref>
        ]. The modeling of time-based maps
has been discussed in [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]. The authors used a combination of the web annotation model, together
with GeoSPARQL and OWL-Time to annotate textual sources about Australian explorations with
geographical and temporal information. The problem of describing spatial diachronic entities has been
addressed by the SONADUS project [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]. They employ BFO for spatiotemporally structure a dataset
about administrative units of Switzerland, tracking geographical changes and assigning new identity
and geometry over any documented change. Another important research that has touched upon the
topic of this work has been developed as part of the FinnONTOproject. The work of Hyvönen et al [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ]
propose a 4D ontology for the annotation of spatio-temporal regions, where each spatiotemporal slice
representing the region is recorded as an individual. The collection of spatiotemporal slices defines
the identity of a region. The ontology has been used to describe the municipalities of Finland in the
period 1865–2010. More recently, the French project Social Dynamics in Urban Context has created
a geohistorical knowledge graph based on named entities extracted from 19th-century Parisian trade
directories [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ]. The project uses the LOCN ontology1 to annotate each address, and PAV2 to link each
statement to the trade directory that documents it. Charles and Hernandez [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ] have recently proposed
an ontology for representing hierarchical historical territories (HHT) and their evolution, division, and
changes.
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Use Case</title>
      <p>Exhibition data can be modeled theoretically (top-down) or by analyzing how they are described in
existing information structures (bottom-up) [15]. The latter is more efective because it adheres to
the concreteness of the data and encourages a culture of reuse. In line with this approach,
selecting a dataset that captures a wide variety of exhibition information was crucial. With this objective
in mind, BasArt—a comprehensive, collaborative database of exhibition catalogs—was chosen as the
guiding model. Developed under the aegis of the Artl@s project3 [16], BasArt provide researchers
access to a wealth of information. At the time of this writing, BasArt documents 5653 exhibitions
from the 19th century to the present day. Exhibition information is extracted from digitized catalogs
using semi-automatic methods, and subsequently datified, normalized, and inserted in a SQL database.
Every record is registered in the base using a comprehensive set of descriptors including temporal
information about the exhibition, artwork exhibited and by whom, as well as many details of the artists
involved. The recorded data focus mainly on four entities, the exhibition itself, its participants (artists),
the artwork exhibited and the source used for the description (catalog). Given its global focus and the
presence of diverse types of historical and contemporary exhibitions, BasArt has been the perfect use
case to develop for model integrating and examining exhibition data. Due to its popularity within
memory institutions, the data has been modeled using CIDOC-CRM, a bottom-up, event-centric, domain
1https://semiceu.github.io/Core-Location-Vocabulary/
2https://pav-ontology.github.io/pav/
3https://artlas.huma-num.fr
ontology created under the aegis of ICOM (International Council of Museums). CRM aims to provide
a way to formalize statements about human activities, and specifically their interactions with heritage
objects and practices [17]. It purposefully uses a neutral formalism, in order to be implemented using
diverse encoding (e.g., database schemas, rdf, neo4j schemas). CRM is actively developed through the
CRM-SIG (Special Interests Group), and the last version available is 7.3. Aside from the core classes
and properties, CRM has been extended to cover multiple domains. Particularly useful to the context
of this paper is the extension developed for documentation of spatiotemporal phenomena [18].</p>
    </sec>
    <sec id="sec-4">
      <title>4. Context</title>
      <p>Due to space constraints and the complexity of the subject, this paper focuses on a specific aspect
of modeling, expressing the temporal validity of diachronic spatio-temporal features. Specifically, we
will focus on one, seemingly simple, ontological pattern: the address. Exhibition catalogs ofer valuable
historical data about the artistic community, detailing who participated in an exhibition, when it took
place, which artworks were displayed and, most importantly, where the artist may have resided at
the time (see example in Fig. 1). These catalogs serve as historical records, indicating that within a
specific period, an artist was associated with a particular address. However, the context of this address
remains unclear—it could represent the artist’s studio, residence (often the same as the studio), or
simply a correspondence address. Despite this ambiguity, each artist’s entry gives us key data on the
spatial and temporal distribution of the artistic community within a city.</p>
      <p>Nevertheless, this information has a significant limitation, as the addresses recorded are valid only at
the time of the exhibition’s opening. As addresses change over time, a later exhibition might associate
the artist with a diferent address. To better understand the problem we can use the example ( EX1) of
the artist Albert Marquet. The famous French painter has participated in a large number of exhibitions,
and by studying exhibition catalogs we are able to retrace the addresses he used over the years. In
the catalog of the 19e Société des Indépendants, published in 1903, he provided as address ‘62, rue
Bargue, Paris’. The next year, in 1904, the catalog of the 20e Société des Indépendants revealed that his
address changed to ‘211 bis avenue de Versailles, Paris’. According to the catalog of the 23e Société des
Indépendants, held in 1907, his address changed again, this time in ‘29, place Dauphine, Paris’. Finally,
in the catalog of the 24e Société des Indépendants, held in 1908, Albert Marquet’s address was ‘19 Quai
Saint-Michel, Paris’. If some catalogs are rich in details, others do not report any address information.
It is the case of the Katalog der Fünfzehnten Ausstellung der Berliner Secession, Berlin in 1908 and
in the International Exhibition of Modern Art Association (Armory Show) in 1913. Marquet appears
in both catalogs but without any indications regarding his current residence, although we know from
the catalog of the 24e Société des Indépendants that in 1908 he was living in 19 Quai Saint-Michel in
Paris. Simply recording in a database the list of addresses used by an artist during their career is surely
useful, but will provide us with quite limited insights into their activities, as we would not be able to
explore the temporal dimension of the artist’s movement. The key information to record is when each
address was in use by an artist. Although this information is not explicitly stated in the catalog’s artist
entry, we can infer it from the exhibition itself. Each entry, in fact, can only be considered accurate
and valid within the timeframe of the exhibition, as we cannot determine if the presence of an artist at
an address is true or false outside of their initial statement. Hence, the relationship between address
and artist is temporal, it exists in time. To complicate the matter further, the address itself is also a
diachronic entity, it comes into existence and eventually ceases to exist. Streets can be reclassified,
or become part of a new municipality or borough. For instance, (EX2) the artist Théodore Béthume,
according to the ’Salon des Artistes Français’ of April 1852, lived in ’rue de La Villette, 4’ in Belleville,
a municipality that only a few years later would become part of Paris. Another artist, (EX3) Simone
Perrin, in the catalog of the ’39e exposition de la société des artistes indépendants’ in 1928 indicated
the address ’38, avenue du Parc-Montsouris’. While it was its correct name at the time, it was later
renamed ’Avenue René-Coty’. Given this level of information richness and complexity, it is essential
to develop a model capable of sustaining information about historical changes over physical entities,
applicable to the many contexts that work with temporally constrained facts, specifically facts about
dynamic physical and spatial entities.</p>
    </sec>
    <sec id="sec-5">
      <title>5. Modeling the Validity of Spatiotemporal Statements</title>
      <sec id="sec-5-1">
        <title>5.1. Requirements and Objectives</title>
        <p>As described in the section above, addresses are complex entities that are inherently paired with the
person who inhabits them, as they are used not as mere identifiers of a place, but to identify the
person who lives in that place. For such reason, they are always a fluent, i.e. a relationship between
a person and place that holds for a specific time interval [ 19]. A model for documenting addresses
should be structured in order to be capable of formalizing statements about a person’s temporary
presence within a specific spatiotemporal segment. Consequently, we should be able to document the
temporary presence  x of an artist  x at a specific location  x during the time ( 0 −  1), recording both
the location’s current and/or historical name of  x ( x( x,  0…n)) as needed. Since we are working
with historical sources ( x), it is crucial to reference the origin of the statement, in this case, the catalog
( x( ) ) that documents the exhibition ( t0..n ).</p>
        <p>With these requirements in mind, we can establish three challenges: (CH1) Formalize the temporal
validity of an address provided by an artist in an exhibition catalog; (CH2) Formalize the diferent
names given to an address in time; (CH3) Facilitate the extraction of a list of artists who indicated
the same address in the same time period. We will examine three ontological patterns representing
three diferent methods to tackle these challenges. Section 5.2 uses binary relationships to express
temporal validity with the aid of RDF-star; section 5.3 presents a partial endurantist modeling, relying
on CIDOC-CRM and n-ary construct; section 5.4 present a full endurantist model applied to CRM.</p>
      </sec>
      <sec id="sec-5-2">
        <title>5.2. LOCN and Tempo</title>
        <p>It is possible to encode the address and its temporal validity using two ontologies, LOCN and TempO.
TempO or Temporal Ontology4, formalizes a set of classes and properties for documenting valid time
and decision time for bitemporal and tritemporal databases. LOCN is an ontology for the description
of the fundamental characteristics of a location. It is part of the Core Vocabularies defined in the
context of the European Union. By combining TempO and LOCN we can express the temporal validity
of a recorded address. However, it is important to note that what is considered valid is not the
address itself, but the relationship between a person and that address. This type of statement requires
more than two predicates ( (  ,    ,  ) ), and since RDF 1.1 does not support the
representation of higher arity predicates, we must define a method to express this statement using one
of the various available approaches [20, 21, 22, 23]. Among the diferent methods available, the one
chosen is RDF-star, as it is (although diferently) largely supported by rdf graph databases, it has been
chosen as a base for RDF 1.2 and, it provides a less cumbersome approach to reification as well as an
easy-to-understand serialization. RDF-star provides a compact alternative to standard RDF reification,
extending the model with a new construct, quotedTriple. A quoted triple is a triple used as the subject
or object of another triple. Therefore, an artist’s address can be represented with a traditional triple
&lt;s&gt;&lt;p&gt;&lt;o&gt;. Using RDF-star we use such triple as the subject of (quotedTriple) of other triples. By doing
so, we can further specify the validity of the original statement using a predicate from TempO, such
as tempo:validFrom or tempo:validTill (see example in Listing 1). Using the same approach we
can assign a temporal frame to street names and toponyms5. This approach captures the time-bound
nature of spatial features.
&lt;&lt; &lt; e x : Marquet &gt; c v : d o m i c i l e &lt; e x : a d d r e s s M a r q u e t &gt; &gt;&gt; tempo : v a l i d F r o m
” 1 9 0 3 − 0 4 − 0 1 ” ^ ^ x s d : d a t e &gt;&gt; c i t o : i s D o c u m e n t e d B y b a s : c a t a l o g 8 9 4 .
&lt; e x : a d d r e s s M a r q u e t &gt; l o c n : f u l l A d d r e s s ” 6 2 , r u e B a r g u e , P a r i s ” .
Listing 1: Example of RDF-star. The statements constrain the validity of a Marquet’s address to a time
period. Prefixes used are listed on prefix.cc .</p>
        <p>Using LOCN and TempO in combination with RDF-star we can express the temporal validity of an
address (CH1), the various names it has been given over time (CH2), and, using SPARQL-star, retrieve
information about artists who have shared the same address (CH3). From a modeling perspective,
RDF-star ofers tremendous potential for streamlining the expression of historical changes in an
easyto-understand manner.</p>
      </sec>
      <sec id="sec-5-3">
        <title>5.3. Fluents and CIDOC-CRM</title>
        <p>Starting from version 5.1.2, released in October 2013, CRM introduced the concept of
E92 Spacetime Volume, shifting from a fully endurantist perspective to a partial perdurantist one.
The change made it possible to link physical entities with spatiotemporal volumes. Using these classes
and properties we can formalize statements about a person’s temporary presence within a specific
spatiotemporal segment. The proposed model (Fig. 2) showcases how we can use CRM to document the
temporal presence of an artist within a specific address. To understand the possibilities and limitations
of the model, and its possible uses for the formalization of dynamic spatio-temporal features, we can
examine closely the choices about its diverse components.</p>
        <p>Spatio-temporal segment( x). The spatio-temporal segment representing the person using an
address is encoded as an instance of the class crm:E93_Presence. This class formalizes a snapshot of
5A full example is given in https://gist.github.com/ncarboni/ba04250bbc9a2ed0c5953a156d5ccdee
a crm:E92_Spacetime_volume, a restricted part of a larger volume chosen to determine and record
the extent of a phenomenon. In the modeling, instances of crm:E93_Presence are linked to both
spatial and temporal projections, respectively the address of the artist and the exhibition’s timespan.
Since addresses serve as contact points rather than definitive indicators of presence, it is uncertain
whether the artist was actually at the address during the exhibition. Consequently, the temporal
projection only records the partial and temporary presence (crm:P197_covered_parts_of) of an actor
at a given address (crm:E53_Place). Each address used by an artist can be modeled as an instance of
crm:E93_Presence</p>
        <p>Source( x). The connection to the source is crucial in a historical context. For such reason,
each spatiotemporal segment representing an artist living in a specific address should be linked
(crm:P70i_is_documented_in) with the document(s) (crm:E31_Document) which serves as the source
for the recorded statement.</p>
        <p>Temporal Projection( 0 −  1). The temporal information of the presence (crm:E93_Presence), i.e.
the segment representing the person using an address, is specified using crm:E52_Time-span. In this
instance, since our knowledge of the address is based solely on the details provided by the exhibition
(crm:E7_Activity) catalog, the timespan associated with the spatiotemporal projection always aligns
with that of the exhibition.</p>
        <p>
          Spatial Projection( x). The spatial projection is modeled as an instance of crm:E53_Place. To
make use of the capabilities of GeoSPARQL-compliant Graph Stores, the data have been further aligned
to the GeoSPARQL ontology6. There exists already a mapping between CIDOC-CRM and GeoSPARQL
in the CRMgeo extension [24, 18]. A more detailed representation of the interconnection between
the two is given in Table 1. The author believes there are a few steps still missing for completing
an integration between GeoSPARQL and CRM. A few properties for geometric serialization are not
mapped with GeoSPARQL (see Table 2), and an important serialization (geo:asGeoJSON) is not yet
present. Additionally, the mapping lacks a foundation in CRM itself. The class crm:E53_Place, for
instance, is not mapped yet, and within the community, there is a lack of clarity about its ontological
status (see the diferent mappings CRM-GeoSPARQL in [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ] and [25]). Due to these reasons, the model in
Fig. 2 formalizes the geometry of the address using GeoSPARQL. By instantiating the spatial projection
as both crm:E53_Place and geo:Feature it is possible to use the GeoSPARQL ontological pattern for
the definition of a geometrical serialization.
        </p>
        <p>The diagram in Fig. 2, presents a CRM-way to formalize spatiotemporal presence. Each time a
catalog documents an artist residing at a particular address we can instantiate it as a crm:E92_Presence,
which is going to be further linked to a spatial and temporal dimension. The latter represented as
crm:E52_Time-span, provides us with an easy mechanism for distinguishing when artists occupied the
same space. The spatial dimension represents the address, formalized as an instance of crm:E53_Place
with an associated WKT geometry (Point). Each address, defined by its street name and street number,
is encoded as an individual entity with a unique IRI, thereby facilitating the identification of situations
6Documentation at https://docs.ogc.org/is/22-047r1/22-047r1.html
where two artists share the same address. A limitation of this approach is the need for constant data
curation, which is not always feasible, especially as new catalogs are frequently added to BasArt.
However, by utilizing the GeoSPARQL ontology, we can efectively apply its functions at the query level.
For instance, the geof:distance function allows us to retrieve artists who have used the same address
by calculating the distance between documented geometries, while the geof:nearby function returns
all geometries within a specified radius of a given point. Moreover, when the dataset is curated, the
geof:sfContains function can be employed to query artists residing within specific districts, streets,
or any defined bounding box.</p>
        <p>Using this model, we can systematically document the various addresses associated with an artist
throughout their lifetime. To enhance data usability, the model in Fig. 2 integrates a simple and
complex layer. The basic exhibition information is organized within a ‘simple layer,’ an
ontological pattern that provides users seamless access to the data. This layer links the exhibition, its
timeframe, the address, the residing artist, and the historical source, allowing retrieval without
requiring knowledge of the underlying spatiotemporal modeling. For instance, using the property
crm:P74_has_current_or_former_residence we can easily retrieve the list of documented addresses
associated with an artist without having to further navigate the graph. However, by using the class
crm:E93_Presence we can change the shape in which the same information is linked together,
providing a way to query the spatiotemporal presence of an artist at each documented address. The two
modeling solutions help provide easy access to CRM data while maintaining an information-rich
environment for domain specialists who may want to extract as many details as possible from the dataset.</p>
        <p>The modeling in Fig 2, while satisfying the requirements of CH1 and CH3, needs more details for
CH2. In fact, the address is modeled only as a static entity. Given the examples in EX2 and EX3 it
is essential to develop a model capable of recording the dynamicity of an address. The mapping in
Fig 2 is complemented by the one in Fig. 3, which illustrates how to use CRM spatiotemporal classes
to formalize the temporal validity of street names and municipalities. The model formalizes the
address as the geometrical projection of a spatiotemporal segment. This makes it possible to record and
link its diferent phases, instantiated as crm:E93_Presence, specifying for each phase its temporal
attributes as well as the name used during the phase (as in EX3). CRM formalizes a series of properties
for expressing time relationships (similarly to Allen operators), but only for the class of temporal
entities (crm:E2_Temporal_Entity). As spatiotemporal entities and temporal entities are classified under
separate branches of the taxonomy, we cannot use these properties to express relationships between
spatiotemporal segments. Due to the issue, it is not possible to express with CRM that one address was
used earlier than another. Since such relationships are not defined in CRM, we formalize them using
OWL-Time7.</p>
        <p>We can still rely on CRM to express the relationship between an instance representing the geometry
of the address and an instance representing the municipality it belongs to (CH2). As done for the
address, we can also document its diferent phases, instantiated as crm:E93_Presence, and specify
for each of them its corresponding label and temporal attributes. This makes it possible to describe
EX2, documenting that an address at time  belongs to a municipality that, at the same time  , was
identified with a specific label.</p>
      </sec>
      <sec id="sec-5-4">
        <title>5.4. 4D Fluents</title>
        <p>The perdurantist logic of CIDOC-CRM difers slightly from other 4D ontologies [ 26, 19]. Unlike full
perdurantist 4D ontologies, not all entities in the CRM are of a temporal nature. Physical entities
”deifnes a spacetime volume unique to it ” [27] but as a matter of identity they are still considered instances
of E77 Persistent item, endurants, disjoint from perdurants, which are formalized as instances of
the class E2 Temporal Entity. In the current incarnation of the ontology, version 7.3, endurants (and
persons) preserve their identity in time. Their identities are linked with a spacetime but they are not a
spacetime themselves. In perdurantist ontologies entities are understood as perdurants, i.e. 4-d ’slice’
of a larger hypervolume of 4-dimensional space [28]. We do not document statements about the entity,
but about the entity’s temporal part. Given their time-related nature, perdurantist ontologies appear
to be quite promising for the description of historical phenomena. To investigate their use, this section
presents a hybrid approach combining the 4D ontology8 with CRM.</p>
        <p>The 4D ontology is encoded to be a lightweight top ontology, and it formalizes only a few classes to
encode temporal slices of entities and their extent in time. It takes the perdurantist stance that entities
have a diachronic identity (they are diferent at every documented time), and assertions about entities
should be always framed in time. Each temporal part of an entity is encoded as an individual with a
time extent, and each statement encoded with the ontology is a temporal statement [26]. We can
combine this approach with CRM, by classifying the top classes in the CRM taxonomy (crm:E53_Place,
crm:E77_Persistent_Item and crm:E2_Temporal_Entity) and the top properties as, respectively,
subclass of 4d:TemporalPart and subproperties of 4d:temporalProperty. In such a way, we
formalize all the mentions of the same address found in the exhibition catalogs as temporal parts of the same
entity, separate individuals that are associated with one or multiple artists (see example in Fig. 4).
Artists are also space-time worms. A record in a catalog in 1901 mentioning that ”Marquet live in 38
8https://www.emse.fr/ zimmermann/ndfluents.html
rue Monge, Paris” should refer not to Marquet himself, but to the ”Marquet living in 1901”. In the same
way, the statement would not refer to the entity representing ’38 rue Monge, Paris’, but its 4D slice, 38
rue Monge existing in 1901. The entity Marquet, for instance, would be constituted by the collection
of all the recorded facts about him in the base. In our example, all the statements about the addresses
associated with him would be data points that constitute its identity: Marquet1903(62, rue Bargue),
Marquet1904(211 bis avenue de Versailles), Marquet1907(29, place Dauphine), Marquet1907(19 Quai
Saint-Michel). The context of each of these statements is always temporally bound, as the
information recorded is limited to the documented timeframe, reflecting a source-first approach. Using this
modeling voids the validity problem (CH1), as the statements regarding the presence of each artist
are framed in time. The property crm:P74_has_current_or_former_residence, in fact, connects a
version of the artist existing in   with a version of the address also existing in   . The documentation
of diachronic places (CH2), such as in (EX2) and (EX3), would simply document diferent temporal
segments of such places, annotating them with the corresponding historical information valid at the
time. The same can be said for the representation of artists sharing the same address (CH3). With
these models defined, the next section will compare their efectiveness for the presented use case.</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>6. Analysis</title>
      <p>The modelings proposed above present diferent ontological patterns for the representation of
temporally constrained facts. Following a classification by Hayes [ 28], they can be classified into three
patterns: the one in section 5.2 uses a 3D modeling pattern, the one in section 5.3 a 3D+1, and the one
in section 5.4 a 4D. Among the three diferent modeling proposed above, only the one in section 5.2
express explicitly the validity of a recorded address. The CRM modeling does annotate the validity,
although implicitly. The recorded propositions are, in fact, contained, and thus valid, within a
determined spatiotemporal frame. The modeling in section 5.4 does not explicitly annotate the validity of
the assertions, since the documented entities referred to already possess temporal boundaries. Any
of the along modeling successfully retrieves the address and its temporal boundaries, however with
some diferences. The ontological pattern proposed in section 5.2 does express the validity of the
statement but with very little semantics. The richness provided by the myriad of properties and classes in
CIDOC-CRM is, of course, incomparable with the basic vocabulary used here. However, such richness
is not always necessary, and its usefulness depends on the scope of the data modeling. If the primary
objective is analytical rather than documentative, this solution is particularly efective, as it preserves
the structure of the data while ensuring a lean and eficient dataset. Moreover, this type of pattern is
considered to be the most user-friendly and easy to adopt [29]. The only two limitations to be
considered are (i) the presence of few RML mappers that support RDF-STAR and (ii) the possible complexity
in querying when dealing with highly nested triples, specifically for non-computer scientists (e.g., art
history/heritage researchers). The 4D perdurantist logic proposed in section 5.4 is a perfect solution
for documenting historical knowledge, as it takes into account the dynamicity of entities that represent
historical objects and events. However, there are some drawbacks at the application level. The method
can produce a very high proliferation of time slices [30], and therefore the creation of a very large
quantity of triples that may hinder both reasoning and retrieval of the data. Another problem of the pattern
proposed in section 5.4 is that is regarded, by a qualitative study on data modelers [29] as the most
complicated ontological pattern to use. The CRM solution proposed in section 5.3 strikes a middle
ground, as it does present the possibility to map the data with spatiotemporal properties without
creating a massive proliferation of time slices as in the 4D approach. The result is far from lean, but it has
the great advantage of working alongside the CRM universe, immediately aligned with the rest of the
model, and many other cultural heritage linked data resources. A great advantage of CRM is that it
better conveys the nuances in historical statements, due to its connection with humanist practitioners and
scholars. The distinction between the properties crm:P197_covered_parts_of, which describes the
partial or complete overlap of a time slice with a spatial extent, and P161_has_spatial_projection,
which refers to the coverage of a spatial extent by a spacetime volume, exemplifies the nuanced
distinctions embedded in the ontology. Such subtleties may appear less relevant in the case of large-scale
data-driven applications, but they are highly valued by humanists. The presence of a large number of
nuanced properties, while highly regarded by data owners, can create quite dificult models to query
and fully comprehend. It is particularly dificult, specifically for new users on CRM, to strike the
balance between expressiveness and practicality. That being said CRM, due to its ontological richness and
widespread adoption in the cultural heritage domain, it will increase the potential for data reuse and
integration across diferent digital humanities sources. For such reason, it is the preferred modeling
choice for BasArt, although more tests are necessary to understand how its integration with a full 4D
framework would help data representation.</p>
    </sec>
    <sec id="sec-7">
      <title>7. Conclusion</title>
      <p>This paper presented a framework for modeling the temporal validity of artist-recorded addresses as
documented in exhibition catalogs. Through the comparative analysis of three ontological patterns—
RDF-star, CIDOC-CRM, and a 4D ontology— the contribution has demonstrated various approaches
that efectively capture the diachronic nature of addresses. Each method ofers distinct advantages.
RDF-star provides an easy-to-understand, lean, and eficient solution that is ideal for analytical tasks.
CIDOC-CRM ofers a balanced approach that aligns well with existing cultural heritage resources,
ofering a rich semantic depth and numerous nuanced distinctions that are particularly valuable in
humanities research. The 4D ontology, while potentially adding complexity to data management,
offers comprehensive representational power and flexibility and, moreover, it aligns closely with the
underlying thinking of historical research. The three patterns are conceived to be used for structuring
and retrieving information about historical changes over physical entities and can be applied to the
many contexts that work with temporally constrained facts, specifically facts about dynamic physical
and spatial entities. Further research should investigate the computational diferences, in terms of
transformation and analysis between the three models, providing quantitative (e.g. number of triples
produced, query performance, eficiency, reasoning time) and qualitative metrics (e.g., user studies on
querying 4D data vs 3D vs 3D+1) to guide data modelers in selecting the most appropriate approach
for their case study.</p>
      <p>The CIDOC-CRM pattern discussed in section 5.3 has been used to transform a large dataset of
artists’ addresses from the BasArt database into RDF. This work has made it possible to extract temporal
information about each artist’s residency along with any address documented in the data, which in turn
enables us to examine the temporal and spatial distribution of the artistic communities in 20th century
Paris.</p>
    </sec>
    <sec id="sec-8">
      <title>8. Bibliography References</title>
      <p>Humanities, in: Formal Ontology in Information Systems, IOS Press, Sherbrooke, QC, Canada,
2023, pp. 257–271. doi:10.3233/FAIA231133.
[15] M. Fernández-López, A. Gómez-Pérez, N. Juristo, Methontology: From ontological art towards
ontological engineering, in: AAAI-97 Spring Symposium Series, volume Proceedings of the
Ontological Engineering AAAI-97 Spring Symposium Series, American Association for Artificial
Intelligence, 1997.
[16] B. Joyeux-Prunel, O. Marcel, Exhibition catalogues in the globalization of art. A source for social
and spatial art history, Artl@s Bulletin 4 (2015) 8.
[17] G. Bruseker, N. Carboni, A. Guillem, Cultural Heritage Data Management: The Role of Formal
Ontology and CIDOC CRM, in: Heritage and Archaeology in the Digital Age, Quantitative
Methods in the Humanities and Social Sciences, Springer, Cham, 2017, pp. 93–131.
[18] G. Hiebel, M. Doerr, Ø. Eide, CRMgeo: A spatiotemporal extension of CIDOC-CRM, International</p>
      <p>Journal on Digital Libraries 18 (2017) 271–279. doi:10.1007/s00799- 016- 0192- 4.
[19] C. Welty, R. Fikes, A Reusable Ontology for Fluents in OWL, in: Formal Ontology in Information</p>
      <p>Systems, IOS Press, 2006, pp. 226–236.
[20] D. Hernández, A. Hogan, M. Krötzsch, Reifying RDF: What works well with wikidata, in:
Proceedings of the 11th International Workshop on Scalable Semantic Web Knowledge Base Systems,
volume 1457, CEUR-WS, Bethlehem, PA, 2015, pp. 32–47.
[21] O. Hartig, Foundations of RDF* and SPARQL* : (An Alternative Approach to Statement-Level
Metadata in RDF), in: AMW 2017 11th Alberto Mendelzon International Workshop on
Foundations of Data Management and the Web, Montevideo, Uruguay, June 7-9, 2017., volume 1912, Juan
Reutter, Divesh Srivastava, 2017.
[22] V. Nguyen, O. Bodenreider, A. Sheth, Don’t like RDF reification?, in: 23rd International World
Wide Web Conference (WWW 2014), volume Proceedings of the 23rd international conference
on World wide web, Association for Computing Machinery, 2014, pp. 759–770. doi:10.1145/
2566486.2567973.
[23] J. J. Carroll, C. Bizer, P. Hayes, P. Stickler, Named graphs, provenance and trust, in: Proceedings
of the 14th International Conference on World Wide Web, WWW ’05, Association for Computing
Machinery, New York, NY, USA, 2005, pp. 613–622. doi:10.1145/1060745.1060835.
[24] M. Doerr, G. Hiebel, CRMgeo: Linking the CIDOC CRM to GeoSPARQL through a Spatiotemporal</p>
      <p>Refinement, Technical Report 435, ICS-FORTH, 2013.
[25] V. Ducatteeuw, Developing an urban gazetteer : A semantic web database for humanities data,
in: GeoHumanities’21 : Proceedings of the 5th ACM SIGSPATIAL International Workshop on
Geospatial Humanities, Association for Computing Machinery, Beijing, China, 2021, pp. 36–39.
doi:10.1145/3486187.3490204.
[26] J. M. Giménez-García, A. Zimmermann, P. Maret, NdFluents: An Ontology for Annotated
Statements with Inference Preservation, in: E. Blomqvist, D. Maynard, A. Gangemi, R. Hoekstra,
P. Hitzler, O. Hartig (Eds.), The Semantic Web, Springer International Publishing, Cham, 2017, pp.
638–654. doi:10.1007/978- 3- 319- 58068- 5_39.
[27] C. Bekiari, G. Bruseker, C. Erin, M. Doerr, P. Michon, C. E. Ore, S. Stead, A. Velios, CIDOC
Conceptual Reference Model, 2024.
[28] P. Hayes, Formal Unifying Standards for the Representation of Spatiotemporal Knowledge,
Technical Report 02TA4-SP1-RT1, Florida Institute for Human &amp; Machine Cognition, 2004.
[29] A. Scheuermann, E. Motta, P. Mulholland, A. Gangemi, V. Presutti, An empirical perspective
on representing time, in: Proceedings of the Seventh International Conference on Knowledge
Capture, K-CAP ’13, Association for Computing Machinery, New York, NY, USA, 2013, pp. 89–96.
doi:10.1145/2479832.2479854.
[30] V. Zamborlini, G. Guizzardi, On the Representation of Temporally Changing Information in
OWL, in: 2010 14th IEEE International Enterprise Distributed Object Computing Conference
Workshops, 2010, pp. 283–292. doi:10.1109/EDOCW.2010.50.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>F.</given-names>
            <surname>Vogel</surname>
          </string-name>
          ,
          <article-title>On the canon of exhibition history, in: Re-Envisioning the Contemporary Art Canon</article-title>
          , Routledge, London,
          <year>2016</year>
          , pp.
          <fpage>205</fpage>
          -
          <lpage>218</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>B.</given-names>
            <surname>Altshuler</surname>
          </string-name>
          , Salon to Biennial - Exhibitions
          <source>that Made Art History</source>
          , Volume
          <volume>1</volume>
          :
          <fpage>1863</fpage>
          -
          <lpage>1959</lpage>
          , Phaidon Press, London ; New York,
          <year>2007</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>D. S.</given-names>
            <surname>Greenwald</surname>
          </string-name>
          ,
          <article-title>Painting by Numbers: Data-driven Histories of Nineteenth-Century Art</article-title>
          , Princeton University Press, Princeton,
          <year>2021</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>L.</given-names>
            <surname>Manovich</surname>
          </string-name>
          , Cultural Analytics, Mit Press, Cambridge, Massachusetts,
          <year>2020</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>D.</given-names>
            <surname>Wu</surname>
          </string-name>
          , H.-
          <string-name>
            <given-names>T.</given-names>
            <surname>Wang</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A. U.</given-names>
            <surname>Tansel</surname>
          </string-name>
          ,
          <article-title>A survey for managing temporal data in RDF, Information Systems 122 (</article-title>
          <year>2024</year>
          )
          <article-title>102368</article-title>
          . doi:
          <volume>10</volume>
          .1016/j.is.
          <year>2024</year>
          .
          <volume>102368</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>S.</given-names>
            <surname>Migliorini</surname>
          </string-name>
          ,
          <article-title>Enhancing CIDOC-CRM Models for GeoSPARQL Processing with MapReduce</article-title>
          ,
          <source>in: Proceedings of the 2nd Workshop On Computing Techniques For Spatio-Temporal Data in Archaeology And Cultural Heritage Co-Located with 10th International Conference on Geographical Information Science (GIScience</source>
          <year>2018</year>
          ), volume
          <volume>2230</volume>
          ,
          <string-name>
            <surname>CEUR-WS</surname>
          </string-name>
          , Melbourne, Australia,
          <year>2018</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>B.</given-names>
            <surname>Ranjgar</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Sadeghi-Niaraki</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Shakeri</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.-M.</given-names>
            <surname>Choi</surname>
          </string-name>
          ,
          <article-title>An ontological data model for points of interest (POI) in a cultural heritage site</article-title>
          ,
          <source>Heritage Science</source>
          <volume>10</volume>
          (
          <year>2022</year>
          )
          <article-title>13</article-title>
          . doi:
          <volume>10</volume>
          .1186/ s40494- 021- 00635- 9.
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <given-names>G.-A.</given-names>
            <surname>Nys</surname>
          </string-name>
          ,
          <string-name>
            <surname>M. Van Ruymbeke</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Billen</surname>
          </string-name>
          ,
          <article-title>Spatio-temporal reasoning in CIDOC CRM: An hybrid ontology with GeoSPARQL and OWL-Time</article-title>
          ,
          <source>in: Proceedings of the 2nd Workshop On Computing Techniques For Spatio-Temporal Data in Archaeology And Cultural Heritage Co-Located with 10th International Conference on Geographical Information Science (GIScience</source>
          <year>2018</year>
          ), volume
          <volume>2230</volume>
          ,
          <string-name>
            <surname>CEUR-WS</surname>
          </string-name>
          , Melbourne, Australia,
          <year>2018</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>V.</given-names>
            <surname>Bartalesi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>G.</given-names>
            <surname>Coro</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E.</given-names>
            <surname>Lenzi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Pratelli</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Pagano</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Moretti</surname>
          </string-name>
          ,
          <string-name>
            <given-names>G.</given-names>
            <surname>Brunori</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A Semantic</given-names>
            <surname>Knowledge</surname>
          </string-name>
          <article-title>Graph of European Mountain Value Chains</article-title>
          ,
          <source>Scientific Data</source>
          <volume>11</volume>
          (
          <year>2024</year>
          )
          <article-title>978</article-title>
          . doi:
          <volume>10</volume>
          .1038/ s41597- 024- 03760- 9.
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <given-names>F.</given-names>
            <surname>Yu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E.</given-names>
            <surname>Champion</surname>
          </string-name>
          ,
          <string-name>
            <surname>D.</surname>
          </string-name>
          <article-title>McMeekin, Exploring Historical Australian Expeditions with TimeLayered Cultural Maps</article-title>
          ,
          <source>ISPRS International Journal of Geo-Information</source>
          <volume>12</volume>
          (
          <year>2023</year>
          )
          <article-title>104</article-title>
          . doi:
          <volume>10</volume>
          . 3390/ijgi12030104.
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <given-names>F.</given-names>
            <surname>Gantner</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Waldvogel</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Meile</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Laube</surname>
          </string-name>
          ,
          <article-title>The Basic Formal Ontology as a Reference Framework for Modeling the Evolution of Administrative Units</article-title>
          , Transactions in
          <string-name>
            <surname>GIS</surname>
          </string-name>
          17 (
          <year>2013</year>
          )
          <fpage>206</fpage>
          -
          <lpage>226</lpage>
          . doi:
          <volume>10</volume>
          .1111/j.1467-
          <fpage>9671</fpage>
          .
          <year>2012</year>
          .
          <volume>01356</volume>
          .x.
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <given-names>E.</given-names>
            <surname>Hyvönen</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Tuominen</surname>
          </string-name>
          ,
          <string-name>
            <given-names>T.</given-names>
            <surname>Kauppinen</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Väätäinen</surname>
          </string-name>
          ,
          <article-title>Representing and Utilizing Changing Historical Places as an Ontology Time Series</article-title>
          , in: N.
          <string-name>
            <surname>Ashish</surname>
            ,
            <given-names>A. P.</given-names>
          </string-name>
          Sheth (Eds.),
          <article-title>Geospatial Semantics and the Semantic Web: Foundations, Algorithms,</article-title>
          and Applications,
          <string-name>
            <surname>Springer</surname>
            <given-names>US</given-names>
          </string-name>
          , Boston, MA,
          <year>2011</year>
          , pp.
          <fpage>1</fpage>
          -
          <lpage>25</lpage>
          . doi:
          <volume>10</volume>
          .1007/978- 1-
          <fpage>4419</fpage>
          - 9446-
          <issue>2</issue>
          _
          <fpage>1</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [13]
          <string-name>
            <given-names>S.</given-names>
            <surname>Tual</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Abadie</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Duménieu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Chazalon</surname>
          </string-name>
          , E. Carlinet,
          <article-title>Création d'un graphe de connaissances géohistorique à partir d'annuaires du commerce parisien du 19 ème siècle: Application aux métiers de la photographie</article-title>
          ,
          <source>in: 4es Journées Francophones d'Ingénierie Des Connaissances (IC</source>
          <year>2023</year>
          )
          <article-title>@ Plate-Forme Intelligence Artificielle (PFIA</article-title>
          <year>2023</year>
          )„ Strasbourg, France,
          <year>2023</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          [14]
          <string-name>
            <given-names>W.</given-names>
            <surname>Charles</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Hernandez</surname>
          </string-name>
          ,
          <string-name>
            <surname>HHT:</surname>
          </string-name>
          <article-title>An Ontology to Represent Territorial Dynamics for Digital</article-title>
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>