RCC8 for CIDOC CRM: Semantic Modeling of Mereological and Topological Spatial Relations in Notre-Dame de Paris

Abstract

This work aims at the conceptual and ontological modeling of the abstract spatial relations in heterogeneous cultural heritage data. This work focuses on built heritage, studying the case of Notre-Dame de Paris. The spatial information is a transversal component across the metadata and paradata collection in the datasets about Notre-Dame. The integration using spatial information is crucial for archival, query, analysis, and visualization. Cultural heritage data integration implies the use of the CIDOC CRM ontology, whereas the real-life data challenge the core model because of the complexity of spatial relations. This contribution aims at the analysis of this complexity in terms of mereological and topological spatial relations. It opens an opportunity to explore the conceptualization of space and the abstract spatial relations that go beyond the geometric or the geographic aspects. The contribution presents the conceptual and ontological modeling about the abstract spatial relations using both CIDOC CRM, its extension CRMgeo, geoSPARQL, and RCC8.

Full text

RCC8 for CIDOC CRM: Semantic Modeling of
Mereological and Topological Spatial Relations in
Notre-Dame de Paris
Anaïs Guillem
1
,Antoine Gros
1,2,3
,Kevin Reby
1
,Violette Abergel
1
and Livio DeLuca
1
1UMR CNRS/MC 3495 MAP, Modèles et Simulations pour l’Architecture et le Patrimoine, 13402, Marseille, France
2UMR CNRS 5508, Laboratoire de Mécanique et de Génie Civil, 34090, Montpellier, France
3LISPEN EA 7515, Laboratoire d’Ingénierie des Systèmes Physiques et Numériques, 13100, Aix-en-Provence, France
Abstract
This work aims at the conceptual and ontological modeling of the abstract spatial relations in heteroge-
neous cultural heritage data. This work focuses on built heritage, studying the case of Notre-Dame de
Paris. The spatial information is a transversal component across the metadata and paradata collection
in the datasets about Notre-Dame. The integration using spatial information is crucial for archival,
query, analysis, and visualization. Cultural heritage data integration implies the use of the CIDOC CRM
ontology, whereas the real-life data challenge the core model because of the complexity of spatial rela-
tions. This contribution aims at the analysis of this complexity in terms of mereological and topological
spatial relations. It opens an opportunity to explore the conceptualization of space and the abstract
spatial relations that go beyond the geometric or the geographic aspects. The contribution presents the
conceptual and ontological modeling about the abstract spatial relations using both CIDOC CRM, its
extension CRMgeo, geoSPARQL, and RCC8.
Keywords
Cultural Heritage (CH), Built Heritage, Semantics, spatial, CIDOC CRM, Notre-Dame de Paris, GeoSPARQL,
CRMgeo, RCC8, knowledge graph, ontology modeling, interoperability, IFC, spatial annotation, space,
place, topology, mereology, mereo(topo)logy, ontology, knowledge representation, spatial relations,
spatial cognition
1. Introduction
This contribution is based on the case study of Notre-Dame de Paris as an example of big data in
the cultural heritage (CH) eld. The characteristics of big data for CH are: real-life data, messy,
highly heterogeneous, and specialized in unstructured or semi-structured datasets. The object
of study in cultural heritage is typically tied with both the materiality of objects (buildings,
artifacts) and their non-materiality. The case study of Notre-Dame is no exception: on one hand,
it illustrates the utmost importance of the cathedral as built work, built components, as well
as archaeological artifacts. After the re, the operations of cleaning, extracting, and sorting
SWODCH’23: International Workshop on Semantic Web and Ontology Design for Cultural Heritage, November 7, 2023,
Athens, Greece
$
anais.guillem@map.cnrs.fr (A. Guillem); antoine.gros@map.cnrs.fr (A. Gros); kevin.reby@map.cnrs.fr (K. Reby);
violette.abergel@map.cnrs.fr (V. Abergel); livio.deluca@map.cnrs.fr (L. DeLuca)
0000-0002-1473-7594 (A. Guillem); 0000-0002-2970-8059 (A. Gros)
©2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)

Figure 1: Plan of the ground floor of the cathedral with the nomenclature entities as defined by the
architects of the restoration project (@RNDP).
remains and archaeological workow of inventory, study, and analysis enlighten the porosity
between archaeological methods (excavation documentation, inventory, and documentation),
with operational activities. On the other hand, all the activities for the restoration or the research
on Notre-Dame have in common the characteristic of being spatialized data [
1
,
2
,
3
,
4
]. Thus, the
information about location, space, and place can be understood as shared anchors across highly
heterogeneous datasets and information. The most intuitive and foundational denition of
architecture is the built thing, that is the architecture qua building or built work. Human beings
continuously interact with the built materiality through the non-materiality of space. Space
as emptiness is formed and dened by the materiality that aects its existence. That relation
between fullness and emptiness is what makes possible architecture as lived and experienced
space. The cathedral itself, as architecture, is by essence a spatially complex object [Figure 1].
We will build upon this denition in the rest of this article as scope of modeling about space.
In the perspective of implementing a knowledge graph using CIDOC CRM as integration
ontology for Notre-Dame’s data, the integration using spatial information is crucial. Information
about space and place presents itself as an entry point for the indexing and structuration of
datasets, their enrichment, query, analysis, and visualization [
5
,
6
]. It promotes consistency
within the knowledge base due to the transversality of the spatial question in the documentation
of the spaces of Notre-Dame, the places, the built works and built elements. This contribution
does not focus on the implementation process per se, but rather on the conceptual problems
that emerge from the dierent models and their inherent conceptualizations of space.
The Notre-Dame dataset analysis shows the need for a foundational set of relations that
consistently express spatial relationships in terms of topology and mereology. This question

Figure 2: (a) A photograph taken from the collateral (@Komenda/C2RMF), (b) extract of the nomencla-
ture (@RNDP), (c) section on the interior (@E. Viollet-le-Duc).
goes beyond the location information. The question of space cannot be limited either to its
geographic concept, geometric and GIS information. Plenty of spatial and geometric data is
available but there is a lack of semantics about space and place. Hence, the challenge of the
complexity of spatial relations and data is a multiple level problem that this paper aims to unfold
step by step. To recap, we are looking at how to semantically express the complexity of the
spatial relations in order to have an accurate description of the mereological and topological
spatial relations between built components, spaces, and places in Notre-Dame case study [Figure
2].
Then this work builds upon this real-life data: it aims at the knowledge representation
of the complex spatial relations in heterogeneous cultural built heritage data systematically
expressed. The contribution presents the conceptual modeling of these topological relations
using both the CIDOC CRM (with its extension CRMgeo) and the RCC8. From the scope of the
CIDOC CRM, this modeling is constructed as the interface between RCC8 and CRM to allow
the expression of the needed abstract topological relations. This work is thought in analogy
with existing modeling: rstly, in the CIDOC CRM model, the entity crm:E55_Type acts as a
bridge to SKOS where the thesauri are externally managed. Similarly, the objective is here to
investigate the compatibility between CIDOC CRM and RCC8 models. Secondly, the modeling
of time properties is explicitly inspired from Allen principles: we propose to apply a similar
perspective for the question of spatial relations. In brief, we posit that the RCC8 can play the
role of a semantic module for the topological relationships, in combination with the CIDOC
CRM as domain ontology for the integration of heterogeneous CH data.

Figure 3: Basic CIDOC CRM Properties and classes about spatial relations in CIDOC CRM 7.1.2 [11].
2. State of the Art
The conceptualization and formalization of space and spatial relations are identied as the
speciality of geomatics and geography. The geoinformation community is built around the data
technical workows and implementation of geodata. The manipulation and interoperability of
geodata is made possible with the standardization eort by the OGC Standards Schemas. Orga-
nized as a technical stack, this multi-layered and multi-faceted implementations encompasses
conceptual modelings (ie. Geography Markup Language (GML) [
7
], Keyhole Markup Language
(KML) [
8
]), geometry encodings (ie. Well-Known Text, GeoJSON), services, and standard APIs.
The focus on geoinformation does not t our scope completely because space is conceptualized
as a geographic concept based mostly on 2D representations, geometry and GIS technology [
9
].
The OGC geoSPARQL model serves as an interface to the semantic web for the geoinfor-
mation. The limits in scope of OGC Standard are acknowledged by geoSPARQL as follows:
“GeoSPARQL does not dene a comprehensive vocabulary for representing spatial information.
Instead GeoSPARQL denes a core set of classes, properties and datatypes that can be used
to construct query patterns. Many useful extensions to this vocabulary are possible, and we
intend for the Semantic Web and Geospatial communities to develop additional vocabularies for
describing spatial information” [
10
]. GeoSPARQL is designed as an open model, allowing com-
munities to specify the model to their usage through the addition of vocabularies. In addition,
this design allows an hybridization of the model, whether by the making of an extension or
ontology merging. Nevertheless, the geoSPARQL model is still implicitly bound by the technical
implementation of the 2D space information. Subsequently it bears the same geometric and
geographic representation of the concepts of space.
In the scope of cultural heritage data integration, the CIDOC CRM is a go-to model as a starting
point [
12
]. It is characterized by the central role of the temporal entities and its event-oriented
modeling. The materiality of architectural objects or built works falls under the scope of E18
Physical thing and subclasses, while spaces are rather characterized as instances of E53 Place.
The spatial relations are synthetically described in the introduction of the model [Figure 3]. The

Figure 4: Overview of CRMgeo and GeoSPARQL [13].
base model is expanded by dierent extensions that take into account aspects of spatial modeling.
CRMgeo [
13
,
14
] is to bridge geoSPARQL to CIDOC CRM. It discriminates between phenomenal
and declarative places classes that help dene the relation between space and geometries. To
express spatial relations in CRM, CRMgeo depends on both the CRM spatial relations and
the geoSPARQL interface. Still in the CRM family of models, CRMba [
15
] -b.a. stands for
building archaeology- considers the building as a stratigraphic object from the perspective
of an archaeologist. In stratigraphic analysis, spaces are layered as stratigraphic units. The
formalization of the stratigraphic units of a built works are sketched through mereological
relations and an undened topological relation.
In the Architecture, Engineering and construction (AEC) industry, the standard Industry
Foundation Classes (IFC) dened for Building Information Modelling (BIM) have as powerful
a bias as stratigraphic analysis. The partitioning of spaces is also done from an operational
point of view: the site, building, storey, spaces and elements are dierentiated in a mereological
fashion [
16
]. In the context of semantic web, this model is accessed via ifcOWL [
17
] or replicated
in the Building Ontology Topology (BOT) [
18
]. We can observe here a modelization pattern
similar to the way in which a technical object, such as a STEP model, is partitioned. The main
dierence is that parts of technical objects are interrelated by (mechanical/physical) relations,
dening the interaction, while IFC parts do not rene the interface.
Since the CIDOC CRM is a domain ontology that has been developed bottom-up, the modeling
reects what is the most commonly documented in specic CH elds. We showed the need
for a more generic representation of space or spatial relations. In this direction, the work of
[
19
,
20
] investigates a modeling of foundational relations (FORT) in relation to the most known
foundational ontologies (BFO, DOLCE, UFO). They point out the foundational relational aspect
that is key in spatial relations: Entity-Location, Location, Connection, Parthood, Dependence,
Constitution, Membership, Unity. We identied the need for a similar level of genericity in
relations as in [
19
,
20
] but with the specicity of application domain in cultural heritage, that is
the scope of the CIDOC CRM ontology.
IFC, CRMgeo, CRMba, GIS related models are known models, that means they are operational
and used by specic communities. They carry their own bias in the denition of space and

Figure 5: Schema representing the RCC8 [26] modified (translated).
put their focus on spatial relations as geometry management. The mereological aspect is
systematically taken into account as a hierarchy that can be represented as a tree-like structure.
The topological relations are developed according to operational needs and context, they are
more prone to the modelisation bias. An abstract way to represent them is a graph-like structure.
In built works, entities considered by these relations are heterogeneous (space, built work,
elements.. .), dened by both a geometry or abstract from it. In the next part, we will then
look at the method to express mereological and topological relations between heterogeneous
elements composing space. It will build on the alignment of RCC8 relations with the CRM
model for phenomenal places.
3. Methodology
The objective of this contribution is to model spatial semantics where space is not just understood
as geographic or geometric information as in [21].
We can reason about the relative positions of the entities that make the accounted spaces up.
There are three main categories of spatial relations [
22
]: metric relations, topological relations
and order relations. In this work, we are interested in topological relations. Topology can be
dened as the set of perceived relations that enable us to situate objects in relation to one another.
To be more specic, topology is the study of properties of spaces that are invariant under any
continuous deformation. Thus, topological relationships are the subject of an abundant scientic
literature using a wide range of sound mathematical models [
23
]. The dominant models are:
the 9-IM model (9-Intersection Model), Egenhofer, and the RCC model (Region Connection
Calculus). Basically, these models distinguish several fundamental topological relationships
identied by the Region Connection Calculus (RCC) between spatial entities [
24
,
25
]. The main
dierence between them lies in the dimension of the handled entities. The characterisation of
spaces in buildings consists in identifying 3D regions, whether empty or lled, often presented
in orthogonal projections.

Table 1
The eight spatial relations in RCC8 with labels and definitions.
Symbol Name Note
DC Disconnected
The two regions are completlydisconnected (there are no
common pieces)
EC Externally Connected
The boundaries of the regions touch, but their interiors
are disjoint
PO Partially Overlapping
The two regions partially overlap (there are disjoint sub
parts, and some part of one is included in some part of
the other)
EQ EQual Two regions have the same spatial extent
TPP Tangential Proper Part
The first region is entirely inside the second region and
their boundaries touch each other from the inside
TPPi
Tangential Proper Part In-
verse
The first region contains the second region and their
boundaries touch each other from the inside
NTPP Non-Tangential Proper Part
The first region is entirely inside the second region and
their boundaries do not touche
NTPPi
Non-Tangential Proper Part
Inverse
The first region contains the second region and their
boundaries do not touch
The RCC8 formalism denes eight elementary relationships [Figure 5] to describe spatial
relations between entities whose primitives are regions [Table 1]. [
27
] state that RCC8 for-
malism is dimension independent, applicable in
R𝑛
, and then demonstrate each of the axioms
and subsequent theorems: “The language RCC8 is a widely-studied formalism for describing
topological arrangements of spatial regions. The variables of this language range over the
collection of non-empty, regular closed sets of n-dimensional Euclidean space, here denoted
(𝑅𝐶 +R𝑛)
, and its non-logical primitives allow us to specify how the interiors, exteriors and
boundaries of these sets intersect” [
27
,
28
]. However, the RCC system does not distinguish
between open and closed geometries. Conceptually, human thought is capable of manipulating
abstract notions of openness, such as the interior of a room, a building, etc. [
29
]. Moreover,
Dia Miron points out that inference procedures based on this formalization are not the most
ecient, and reasoning can sometimes turn out to be incomplete or undecidable [30][26].
As explained by [
31
], “Besides CIDOC CRM spatial classes (E53 Place, E44 Dimension, E47
Spatial coordinates and E94 Space Primitives), the model oers properties which fulll most
common topological spatial relations (Dimensionally Extended nine-Intersection Model (DE-
9IM), Region Connection Calculus (RCC8))[...]. Finally, CIDOC CRM denes class E92 Space
Time Volume that designates four dimensional point sets and has temporal (CIDOC:P160)
and spatial (CIDOC:P161) projections. Besides this, the CRMgeo extension provides spatial
and temporal classes and properties dedicated to formulate declarative information. It also
provides links with GeoSPARQL. Indeed, these links with the OGC GeoSPARQL standard
are necessary to make use of the conceptualization and formal denitions that have been
developed in the Geoinformation community” [
31
]. Building upon the same observation, our
approach bears some major dierences: this contribution looks only at spatial relations (instead
of spatio-temporal) for a rather diverse community of architects, archaeologists, conservators,

Table 2
Analysis of the CIDOC CRM properties against the RCC8 relations: we check whether the CIDOC CRM
properties express some topological relationships. We specify if the topology is rather defined in (a) the
scope note, (b) the examples or if it is (c) unspecified.
Domain Property label Range DC EC PO EQ TPP TPPi nTPP nTPPi
E18 P53 has current or former location E53 x(a) x(b) x(b)
E18 P59 has section E53 x x
E18 P156 occupies E53 x(a)
E18 P157i provides reference space for E53 x x x x x x x x
E19 P55 has current location E53 x(a) x(b) x(b)
E53 P53i is former or current location of E18 x(a) x(b) x(b)
E53 P55i currently holds E19 x(a) x(b) x(b)
E53 P59i is located on or within E18 x x
E53 P89 falls within E53 x x
E53 P89i contains E53 x x
E53 P121 overlaps with E53 x x(c) x(c) x(c) x(c) x(c)
E53 P122 borders with E53 x x x
E53 P156i is occupied by E18 x x x
E53 P157 is at rest relative to E18 x x x x x x x x
E53 P168 place is defined by E94 x x(a) x(a)
E53 P171 at some place within E94 x x x
E53 P172 contains E94 x x x
E53 P189 approximates E53 x x x x x x x x
E92 P10 falls within E92 x x x
E92 P10i contains E92 x x x
E92 P132 spatiotemporally overlaps with E92 x x(c) x(c) x(c) x(c) x(c)
E92 P133 spatiotemporally separated from E92 x
E94 P168i defines place E53 x x(a) x
etc. and not for the geoinformation community specically. As shown in the state of the art, the
conceptualization of space and spatial objects diers in terms of scope of application. Similarly
as the modeling about time based on Allen’s principles in CRM or FORT model [
19
,
20
], we
propose to use high level relations to express systematically and consistently the spatial relations
between heterogeneous entities that compose space. For that purpose, we choose to analyze the
compatibility and the possible alignment between the RCC8 and the CIDOC CRM base model.
4. Results
The results of this work are twofold: rst, the analysis of the CIDOC CRM properties in regard
with the RCC8 topological model. Second, the consistency of the modeling is validated against
a sample of Notre-Dame de Paris’ data.
We showed that RCC8 relations are compatible with the heterogeneity of the spatial entities
in cultural heritage built works. We present a survey and analysis of the direct properties of
the CIDOC CRM model in regards to the RCC8 model to highlight the expressivity of the CRM
base model [Table 2]. This survey is grouped by the domains and ranges of the properties: it

Figure 6: Example of spaces mereotopologically related within the Notre-Dame de Paris cathedral
showing the collatéral intérieur 28 [CI28] / interior side of the aisle 28. It is a portion of space in relation
with: files (fr)/ axes (en) [F28] and [F30], travée (fr)/ span (en) [T28], and niveaux (fr)/ storeys (en) [RDC].
Figure 7: Array of spatial relations expressed using the geoSPARQL RCC8 model between heterogeneous
spatial entities with the example presented in [Figure 6] and [Table 2]
shows that spatial properties link few dedicated classes in the CRM model: E18 Physical Thing,
E53 Place, E94 Space Primitive and E92 SpaceTime Volume classes. Only E92 and E53 disposes
of self-referential properties, E53 is both linked with E18 and E94, E92 is isolated from the other
ones. The resulting 4 classes reect the heterogeneity of elements that we posited in our initial
denition of space.
The scope of CIDOC CRM is sucient in most cases [Figure 3]. More comprehensive cases
can arise with cultural heritage built works: we present a sample from Notre-Dame de Paris
cathedral data that illustrates this spatial complexity that comes from both the array of spatial
entities and their mereo-topological relations. As a representative sample, it features a collatéral
(fr) / side-aisle (en) [CI28] as an empty space 3-dimensional region, two les (fr) / axes (en) [F28,
F30] as abstract 2-dimensional regions, one travée (fr.) / span (en) [T28] and two niveaux (fr)
/storeys (en) as abstract 3-dimensional region, building elements pile intérieure (fr) / interior
column (en) [PI28] and its chapiteau (fr) / capital (en) [PIc28] physical as 3-dimensional regions
[Figure 6]. This data sample shows the array of spatial relations considered: mereological and
topological between place-place, place/object and object/object [Figure 7].
This example is a proof of concept for consistent modeling of abstract spatial relations about
built work entities. The aforementioned analysis prevents us from propagating the initial
heterogeneity of CRM spatial entities and properties to the application prole. The CRMgeo
extension provides an in-between for CRM and geoSPARQL that allows us to reach the RCC8

model in geoSPARQL. The sample data and model is available at: https://gitlab.huma-num.fr/gt-
cidoc-crm/architecture-and-built-works-abcrm
5. Conclusion
This contribution was initiated from the case study of Notre-Dame de Paris: the information
about space is crucial in the data integration. While in CH datasets, the information about space
is mostly homogeneous, the Notre-Dame’s spatial data range from microscopic (ie. sample
location) to the scale of an object (ie. a built element), a portion of space, or part of the cathedral.
The scale of the considered spatial objects depends on the type of research question, method,
analysis that are relevant for the dataset. Thus, this range in scale can be seen as a dierent level
of detail in spatial indexing. This led us to go beyond the expression of space as its geometrical
representation. We explored specically abstract spatial relations as a transversal component
for archeological, restoration, and analysis data. The proposed modeling with RCC8 and CIDOC
CRM is checked against a sample of data representing mereo-topological relations between
architectural spaces and built components for a span with collateral and sexpartite vault of the
nave in Notre-Dame de Paris. This subset dataset is used as a proof-of-concept that illustrates
the conceptual modeling as hybridization/composition between models. The exploration is
carried out using an ontological analysis of CIDOC CRM, CRMgeo, geoSPARQL (OGC standard)
focusing on the semantics about space, but not about its geometry. The mereological and
topological relations in the spaces of a built work, as expressed in 2D (plan), but also as volumes
in 3 dimensions and nomenclature.
This article proposed a conceptualization of space from an anthropological perspective of the
lived space. Architecture and space are considered as an experienced built environment and
thus a primordial substrate of material culture. From an operational viewpoint, the modeling of
space as a transversal component enables further operational investigation: interlinking the
dense spatialised information as a network, the organization of the perceived space, description
of engineering system boundaries (ie. thermics, mechanical analysis) and the alignment of
expert systems. The application of this modeling showed its usefulness to the spaces of the
cathedral of Notre-Dame but can be transferred to any built environment and architecture.
Acknowledgments
This work was supported by: the projects REPERAGE and E-RIHS funded by the Fondation des
Sciences du Patrimoine (France), the projects ASTRAGALE and TEATIME funded by the Mission
pour les Initiatives Transverses et Interdisciplinaires of the Centre National de la Recherche
Scientique (France), and the ERC Ndame Heritage funded by ERC advanced Grant 2021. The
authors wish to acknowledge the help and collaborative support from: the chief architects of
historical monuments in charge, Philippe Villeneuve, Pascal Prunet and Rémi Fromont, the
Établissement public chargé de la conservation et de la restauration de la cathédrale Notre-Dame
de Paris (RNDP), and the heritage conservators. The authors thank the numerous scientic
partners and collaborators from the research groups working on Notre-Dame de Paris cathedral,
with special recognition for the Digital Data working group.

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