=Paper=
{{Paper
|id=Vol-258/paper-34
|storemode=property
|title=Combining OWL with RCC for Spatioterminological Reasoning on Environmental Data
|pdfUrl=https://ceur-ws.org/Vol-258/paper17.pdf
|volume=Vol-258
|dblpUrl=https://dblp.org/rec/conf/owled/GrutterB07
}}
==Combining OWL with RCC for Spatioterminological Reasoning on Environmental Data==
https://ceur-ws.org/Vol-258/paper17.pdf
Combining OWL with RCC for Spatioterminological
Reasoning on Environmental Data
Rolf Grütter and Bettina Bauer-Messmer
Swiss Federal Institute WSL, An Institute of the ETH Board,
Zürcherstrasse 111, 8903 Birmensdorf, Switzerland
{rolf.gruetter, bettina.bauer}@wsl.ch
Abstract. A new approach to spatioterminological reasoning is presented which
is based on a hybrid knowledge representation system architecture and on a rep-
resentation of the RCC family tree in OWL. The knowledge base into which the
family tree is imported holds role assertions in terms of RCC-8 relations be-
tween individual regions. It is a key component of a semantic layer constructed
on top of an environmental database which aims at facilitating access to users
by supporting a sophisticated while easy-to-use search engine. Issues of world
assumption and spatial extension to OWL are discussed.
1 Introduction
The core of the Datacenter Nature and Landscape (DNL) of the Swiss Federal Office
for the Environment (FOEN) which is operated by the Swiss Federal Institute for For-
est, Snow and Landscape Research (WSL) is a relational database system implement-
ing a process-oriented data model. It holds data of several inventories of different
kinds of biotopes (bogs, fens, floodplains, grasslands, amphibians spawning grounds,
etc.) which are described using a number of specific terminologies (e.g., botanic, zoo-
logical). A small part of these terminologies has been made explicit in terms of vo-
cabulary used in metadata descriptions. The biotopes cover neighboring or overlap-
ping regions and are further related to non-inventory administrative regions such as
communes or cantons. These regions are described by geometries. Spatial relations
between regions can be computed geometrically by a Geographic Information System
(GIS). However, there is currently no means to make the calculated relations accessi-
ble to logic formalism which is needed in order to process queries combining thematic
aspects with (qualitative) spatial aspects such as “endangered butterflies in Birmens-
dorf and neighboring communes”. This query implies both a spatial expansion,
namely “Birmensdorf and neighboring communes”, and a thematic expansion, namely
“endangered butterflies (in the answer set of the spatial expansion)”, which requires
that the answer set is represented in a way that it can be further processed.
The DNL datacenter holds about 200,000 data records which are grouped into 12
inventories. The number of objects per inventory ranges from some tens to thousands.
Overall, several thousands data records describe spatial objects. Currently, the DNL
datacenter is exclusively accessible to users which have previous knowledge of the
data model and the terminologies used. In order to provide an open and intuitive ac-
2 Rolf Grütter and Bettina Bauer-Messmer
cess also to non-expert users we are constructing a semantic layer on top of the data-
base. This semantic layer integrates an OWL DL knowledge base as a key component
which holds the classes, properties and individuals necessary to semantically and spa-
tially pre-process user input such as search terms before searching the database. The
TBox of the knowledge base holds the thematic terminology which is introduced by
an ontology specifying the users’ conceptualization of the domain. The terminology
also contains the relation names of the different RCC species structured in a hierarchy
of object properties. These names are used to assert selected relations between indi-
vidual regions in the ABox of the knowledge base. We refer to this as a minimal rep-
resentation of RCC in OWL which is motivated by the observation that RCC cannot
be fully expressed, neither in the current version of OWL nor in OWL 1.1, but still
must be minimally represented in order to allow for a combination of terminological
and spatial reasoning services. In this paper we present a new approach to spatioter-
minological reasoning which is based on a hybrid knowledge representation system
architecture and define a minimal representation of RCC in OWL.
The paper is organized as follows: Section 2 provides a short introduction to RCC.
In section 3 we review some related work on the combination of RCC with OWL. In
section 4 we introduce a hybrid knowledge representation system architecture. Spati-
oterminological reasoning based on hierarchies of object properties in OWL is de-
scribed in section 5. Our approach is discussed in section 6.
The work presented here builds on previous work on the design and implementa-
tion of a Web-based platform for visualizing, querying and analyzing environmental
data [1]. It is further related to the virtual database project [2]. Conceptual issues con-
cerning the design of a bilingual eco-ontology for open and intuitive search and of a
hybrid knowledge representation system architecture – the latter with an extensive us-
age scenario for spatioterminological reasoning – have been presented [3, 4].
2 The Region Connection Calculus
The Region Connection Calculus (RCC) is an axiomatization of certain spatial con-
cepts and relations in first order logic [5, 6]. The basic theory assumes just one primi-
tive dyadic relation: C(x, y) read as “x connects with y”. Individuals (x, y) can be in-
terpreted as denoting spatial regions. The relation C(x, y) is reflexive and symmetric.
Using the primitive relation C(x, y) a number of intuitively significant relations can
be defined. The most common of these are illustrated in figure 1 and their definitions
together with those of additional relations are given in table 1. The asymmetrical rela-
tions P, PP, TPP and NTPP have inverses which we write, in accordance with [6], as
Ri, where R ∈ {P, PP, TPP, NTPP}. These relations are defined by definitions of the
form Ri(x, y) ≡def R(y, x).
Fig. 1. RCC-8 relations (for the entire names cf. table 1)
Combining OWL with RCC for Spatioterminological Reasoning on Environmental Data 3
Of the defined relations, DC, EC, PO, EQ, TPP, NTPP, TPPi and NTPPi have been
proven to form a jointly exhaustive and pairwise disjoint set, which is known as RCC-
8. Similar sets of one, two, three and five relations are known as RCC-1, RCC-2,
RCC-3 and RCC-5, respectively: RCC-1 = {SR}, RCC-2 = {O, DR}, RCC-3 = {ONE,
EQ, DR}, RCC-5 = {PP, PPi, PO, EQ, DR}. RCC also incorporates a constant denoting
the universal region, a sum function and partial functions giving the product of any
two overlapping regions and the complement of every region except the universe [6].
Table 1. Basic RCC relations
SR(x, y) ≡def (x, y) (Spatially Related)
C(x, y) (primitive relation) (Connects with)
DC(x, y) ≡def ¬C(x, y) (DisConnected from)
P(x, y) ≡def ∀z[C(z, x) → C(z, y)] (Part of)
O(x, y) ≡def ∃z[P(z, x) ∧ P(z, y)] (Overlaps)
DR(x, y) ≡def ¬O(x, y) (DiscRete from)
EC(x, y) ≡def C(x, y) ∧ ¬O(x, y) (Externally Connected to)
EQ(x, y) ≡def P(x, y) ∧ P(y, x) (EQual to)
ONE(x, y) ≡def O(x, y) ∧ ¬EQ(x, y) (Overlaps Not Equal)
PP(x, y) ≡def P(x, y) ∧ ¬P(y, x) (Proper Part of)
PO(x, y) ≡def O(x, y) ∧ ¬P(x, y) ∧ ¬P(y, x) (Partially Overlaps)
TPP(x, y) ≡def PP(x, y) ∧ ∃z[EC(z, x) ∧ EC(z, y)] (Tangential Proper Part of)
NTTP(x, y)≡def PP(x, y) ∧ ¬∃z[EC(z, x) ∧ EC(z, y)](Non-Tangential Proper Part of)
According to [5], regions support either spatial or temporal interpretation. In case
of spatial interpretation, there is a variety of models among which to choose. The au-
thors provide some examples such as interpreting the relation C (“connects with”) in
terms of two regions whose closures share a common point or stating that two regions
connect when the distance between them is zero.
Table 2. RCC-5 composition table (T(x, z) ≡def {DR(x, z), PO(x, z), EQ(x, z), PP(x, z), PPi(x, z)})
D DR(x, y) PO(x, y) EQ(x, y) PPi(x, y) PP(x, y)
DR(x, z) DR(x, z)
DR(y, z) T(x, z) PO(x, z) DR(x, z) PO(x, z) DR(x, z)
PPi(x, z) PPi(x, z)
DR(x, z) DR(x, z)
PO(x, z)
PO(y, z) PO(x, z) T(x, z) PO(x, z) PO(x, z)
PPi(x, z)
PP(x, z) PP(x, z)
EQ(y, z) DR(x, z) PO(x, z) EQ(x, z) PPi(x, z) PP(x, z)
PO(x, z)
DR(x, z)
PO(x, z) EQ(x, z)
PP(y, z) PO(x, z) PP(x, z) PP(x, z)
PP(x, z) PP(x, z)
PP(x, z)
PPi(x, z)
DR(x, z)
PPi(y, z) DR(x, z) PO(x, z) PPi(x, z) PPi(x, z) T(x, z)
PPi(x, z)
4 Rolf Grütter and Bettina Bauer-Messmer
In order to check consistency of a knowledge base holding spatial relations, so-
called composition tables are used (cf. the composition table for RCC-5 in table 2).
The entries in these tables share a uniform inference pattern which can be formalized
as composition axioms of the general form ∀x, y, z. S(x, y) ∧ T(y, z) → R1(x, z) ∨ … ∨
Rn(x, z) where S, T, and Ri are variables for relation symbols.
A similar approach which is based on the description of topological relations be-
tween two spatial regions was introduced as the 9-intersection model in [7]. In this
model, eight out of nine relations can be interpreted in the same way as we interpret
the RCC-8 relations, namely as spatial relations between polygons in the integral
plane [4]. Only the ninth relation is specific for the model. Given this extensive
agreement on the interpretation of the relations between the two approaches we be-
lieve that the latter, which is axiomatized in first order logic, is easier to combine with
description logics than the first, which is based on a topological framework. The rea-
son therefore is that description logics themselves can be seen as fragments of first
order logic [8].
3 Related Work
A review of existing approaches [9, 10, 11, 12] to combining RCC with extensions to
the description logics ALC is provided in [4]. Since the reviewed extensions and
OWL are not as closely related as one might expect, these approaches cannot be ap-
plied to the Semantic Web without a major revision of the existing Web ontology lan-
guage. However, a major revision is not desirable as an alternate language would
surely miss some of the favorable features of the existing, such as property hierar-
chies, which make it compatible with RDF (Resource Description Framework), the
Web’s description language for resources.
In [13] the authors aim at representing qualitative spatial information in OWL DL.
On the basis of the (assumed) close relationship between the RCC-8 calculus and
OWL DL they extend the latter with the ability to define reflexive roles. The exten-
sion of OWL DL with a reflexive property is motivated by the requirement that such a
property, together with the transitive one, is needed in order to describe the accessibil-
ity relation which relates possible worlds to each of the modal operators of the logic
S4. The modal logic S4 is considered, because the RCC-8 calculus can be translated
into an extension of it [6]. In order to represent RCC-8 knowledge bases the authors
use a translation in which regions are expressed as non-empty regular closed sets. The
RCC-8 relations are then translated into (sets of) concept axioms in OWL DL and the
classes denoted by the introduced concepts are instantiated by asserting for each con-
cept an individual in the ABox in order to ensure that the classes cannot be empty.
While this approach requires only a minimal extension to OWL DL (which has been
considered in the draft to OWL 1.1 [14]), the notion of regions as sets in the (abstract)
object domain (and not in a concrete domain) prevents RCC from effectively combin-
ing with domain ontologies. The reason therefore is that OWL DL requires type sepa-
ration: A class cannot also be an individual (or a property) [15]. However, in order to
classify regions in a domain ontology they must be represented as individuals and not
Combining OWL with RCC for Spatioterminological Reasoning on Environmental Data 5
as concepts.
It seems to be more intuitive to define the RCC relations in terms of role descrip-
tions than to translate them into (sets of) concept axioms. Since current OWL does not
provide constructors for role descriptions (apart from inverse), the underlying descrip-
tion logics have to be extended with these constructors. In [16] it is shown that the ex-
tension of SHIQ with complex role inclusion axioms of the form S D T R is unde-
cidable, even when these axioms are restricted to the forms S D T S or T D S S,
but that decidability can be regained by further restricting them to be acyclic. Com-
plex role inclusion axioms of the unrestricted form are supported by the description
logic SROIQ which serves as a logical basis for OWL 1.1 [17]. However, a closer
look at an arbitrary composition table (except for RCC-1) reveals that, in order to
axiomatize the composition of RCC relations, a language must even support an exten-
sion of the unrestricted form of role inclusion axioms, namely S D T R1 … Rn
(cf. table 2 for RCC-5). If decidability should be preserved, complex role inclusion
axioms are, therefore, not a solution to the translation problem of RCC. Axioms de-
scribing the basic RCC relations even require additional role constructors such as in-
tersection and complement. Extensions of SHIQ with these kinds of role constructors
have, to our knowledge, not been investigated so far. SROIQ supports negation of
roles (i.e., complement) but not intersection.
4 A Hybrid Knowledge Representation System Architecture
Taking into account the result of the review of related work in section 3 we are com-
bining RCC with OWL at the level of the knowledge representation system architec-
ture and not at the level of the formalisms. This implies that the architecture of a
knowledge representation system based on DL is extended with RCC specific compo-
nents.
Fig. 2. Architecture of a hybrid knowledge representation system (adapted from [8], Fig. 2.1)
6 Rolf Grütter and Bettina Bauer-Messmer
Figure 2 shows the architecture of a hybrid system in its simplest form. The grey
shaded components are extensions to the original architecture. The shortcut KB de-
notes the knowledge base. The TBox holds the thematic terminology which is intro-
duced by an ontology specifying the users’ conceptualization of the domain (not
shown). It also contains the relation names of the different RCC species structured in
a hierarchy of object properties. These names are used to assert selected relations be-
tween connecting individual regions in the ABox. The label RCCBox stands for Re-
gion Connection Calculus Box, a term which is inspired by the role box in [11]. The
RCCBox contains the composition tables for RCC-1, RCC-2, RCC-3, RCC-5 and
RCC-8. The RCC reasoner uses the role assertions in the ABox in order to calculate
those pairs of regions which are not connected, and it uses the composition tables in
order to check spatial consistency of the ABox. The dotted arrow pointing from the
RCCBox back to the ABox indicates, that the calculated relations can be asserted in
the ABox in order to speed up the processing of similar queries in the future. Figure 3
shows an acyclic directed labeled graph with the names of the different RCC species
which are structured in a hierarchy of object properties in OWL. By traveling down
the hierarchy from the top to the bottom the relations are successively refined to yield
the different RCC species.
Fig. 3. Representation of the RCC family tree as a hierarchy of object properties in OWL.
Regular arrows represent the rdfs:subPropertyOf property, dotted arrows the
owl:inverseOf property. Nodes in bold face represent relations that can be defined in terms
of OWL DL. Regular nodes represent relations that cannot be defined in terms of OWL DL.
Grey shaded nodes represent the RCC-8 relations.
Combining OWL with RCC for Spatioterminological Reasoning on Environmental Data 7
As figure 3 shows only the relations rcc:inverseProperPartOf,
rcc:inverseTangentialProperPartOf and rcc:inverseNonTangential-
ProperPartOf can be defined in terms of OWL DL. For the majority of relations the
TBox contains necessary but not sufficient axioms of the form RRCC-i+ RRCC-i (i.e.,
rdfs:subPropertyOf) with i+, i ∈ {1, 2, 3, 5, 8} and i+ > i, where RRCC-i+ and
RRCC-i denote arbitrary relations of the species RCC-i+ and RCC-i (cf. table 3 for ex-
amples). Note that because of the transitive property of rdfs:subPropertyOf it
holds that ((R(RCC-i+)+ RRCC-i+) ∧ (RRCC-i+ RRCC-i)) → R(RCC-i+)+ RRCC-i.
5 Spatioterminological Reasoning Based on Hierarchies of
Object Properties in OWL
Even though, in principle, all RCC relations can be geometrically computed and as-
serted in the ABox of an OWL DL knowledge base, it is, for at least two reasons, not
favorable to do so. First, asserting for all pairs of regions all relations holding between
them easily results in a very large knowledge base thereby bearing on the perform-
ance of the system (in our sample the number of asserted relations is roughly one
tenth of the number of a full representation without counting the relations between re-
gions which are not connected; cf. below). Second, as discussed in section 3, since the
inferences implied by the entries in the RCC composition tables cannot be put in
terms of OWL DL axioms [16], an OWL reasoner will be unable to check the consis-
tency of the knowledge base w.r.t. spatial references. For these reasons we argue in
favor of a minimal representation in the ABox of an OWL DL knowledge base and to
infer or calculate those relations which are not represented when requested at runtime.
In order to define a minimal representation of RCC in OWL we assert for all con-
necting pairs of regions in the ABox of a sample knowledge base their relations in
terms of RCC-8. The sample knowledge base holds a (small) part of the knowledge of
the DNL datacenter introduced in section 1. To give an example, partiallyOver-
laps(Albiskette-Reppischtal, Birmensdorf) is one of the 258 RCC-8 relations asserted be-
tween the 44 regions in the knowledge base. Note that in order to keep the number of
asserted relations as small as possible we do not explicitly assert that two regions are
disconnected if they are not connected. 1
Based on this minimal representation a total of 2198 RCC relations can be inferred
from the knowledge base using theorems which share the uniform pattern of the logi-
cal modus ponens: [(RRCC-i+ RRCC-i) ∧ RRCC-i+(x, y)] → RRCC-i(x, y) where RCC-i+
denotes the RCC species from which is inferred and RCC-i the species to which is in-
ferred and x, y denote individual regions. We are using the OWL reasoner Pellet (ver-
sion 1.4, OWL API) in order to access and manipulate the knowledge base.
1 In an upcoming paper we also explore a minimal representation which is based on the primi-
tive RCC relation connectsWith and discuss the soundness and completeness of a calculus for
this representation when compared to a calculus for the herein presented representation.
8 Rolf Grütter and Bettina Bauer-Messmer
Table 3. Terminology and world description introduced to the knowledge base (excerpt)
DL Syntax Semantics
ΔI
Region RegionI ⊆ ΔI
spatiallyRelated spatiallyRelatedI ⊆ ΔI × ΔI
∃spatiallyRelated. Region {a ∈ ΔI | ∃b. (a, b) ∈ spatiallyRelatedI} ⊆ RegionI
∀spatiallyRelated.Region ΔI ⊆ {a ∈ ΔI | ∀b. (a, b) ∈ spatiallyRelatedI → b ∈ RegionI}
overlaps spatiallyRelated overlapsI ⊆ spatiallyRelatedI
overlapsNotEqual overlaps overlapsNotEqualI ⊆ overlapsI
partiallyOverlaps overlapsNotEqual partiallyOverlapsI ⊆ overlapsNotEqualI
Region(Albiskette-Reppischtal) Albiskette-ReppischtalI ∈ RegionI
Region(Birmensdorf) BirmensdorfI ∈ RegionI
partiallyOverlaps(Birmensdorf,
(BirmensdorfI, Albiskette-ReppischtalI) ∈ partiallyOverlapsI
Albiskette-Reppischtal)
Note that from the perspective of RCC the described inference corresponds to a
translation from the relations of the RCC-8 species into the more coarse-grained rela-
tions of RCC-5, RCC-3, RCC-2 and RCC-1. For instance, inferring the theorem [(par-
tiallyOverlaps overlapsNotEqual) ∧ partiallyOverlaps(Birmensdorf, Albiskette-Reppischtal)]
→ overlapsNotEqual(Birmensdorf, Albiskette-Reppischtal) translates the asserted RCC-8
relation partiallyOverlaps(Birmensdorf, Albiskette-Reppischtal) into the RCC-3 relation
overlapsNotEqual(Birmensdorf, Albiskette-Reppischtal) which is not asserted in the knowl-
edge base (cf. table 3). This translation can be useful since a coarse-grained classifica-
tion of relations is easier to handle and might be sufficient for some queries while
others might require a fine-grained classification. The translation also enables agents
speaking different dialects of RCC to communicate with each other.
6 Discussion
Since our minimal representation only asserts connections the OWL reasoner cannot
infer from the asserted relations those pairs of regions which are not connected. One
reason therefore is that OWL DL does not allow negation of roles. Thus, an axiom
like DC(x, y) ≡ ¬C(x, y) is not legal OWL DL (DC stands for “disconnected from”).
However, even if negation of roles were allowed as it is in OWL 1.1 [14], the rea-
soner could not infer for two regions which are not connected that they must be dis-
connected (unless it is explicitly stated). The reason therefore is that OWL DL – like
any description logics – assumes an open world: If two regions are not explicitly
specified as connecting with each other (e.g., by asserting one of the RCC-8 relations)
or as not connecting, their relation to each other is undefined. By combining OWL
DL with RCC the former takes advantage of the closed world of the latter: RCC-8
(and also the other RCC species) forms a jointly exhaustive and pairwise disjoint set
of relations. Any two spatial regions are in one and exactly one of the RCC-8 rela-
tions to each other. This means that in RCC-8 two regions are disconnected if none of
the seven connection relations is asserted for them.
Combining OWL with RCC for Spatioterminological Reasoning on Environmental Data 9
Taking into account the overview of related work which suggests that RCC cannot
be easily expressed even in a future version of OWL we do not argue in favor of a
spatial extension to OWL. Intuitively, it is not surprising that RCC cannot be fully
represented in OWL. Both bear on models for making the real-world accessible to
symbolic manipulation which are not interchangeable (and thus translatable) but
rather complementary. To see the difference it might help to recall the ancient mar-
ketplace. The traded goods could roughly be divided into two distinct categories:
countable goods which were traded by number (e.g., farm animals such as sheep) and
measurable goods (such as flour) which were traded by mass. The first implies the ex-
istence of (identifiable) individuals which can be described in an ontology in accor-
dance with their (assumed) kinship. The second implies the existence of dissective
and cumulative properties which limit the consideration to the mereological notions of
parts and wholes. With reference to individuals, we could denote goods of the second
category as “dividuals” in the proper sense of the word. With regions the matter is
more complex. In a naive sense, they share the dissective and cumulative properties (a
part of a region still is a region and the sum of two (or more) regions still is a region)
but at the same time they can be assigned with a name (or another identifier), distin-
guishing them as individuals. This double nature of regions explains the claims made
by both ontological and mereological approaches, the reconciliation of which is re-
flected, for instance, by the attempts to combine RCC with OWL.
Future work is planned on the verification of the presented approach in the produc-
tive knowledge base of the DNL datacenter introduced in section 1 holding in a first
version 413 spatial regions and on the identification of a minimal temporal represen-
tation for temporal reasoning. The latter will include exploring whether the existing
features of OWL (including OWL 1.1) or of metadata standards like Dublin Core or
ISO 19115 [18] for attributing resources with time labels are sufficiently expressive to
capture the temporal references of environmental data.
Acknowledgements. The authors sincerely thank Jürg Schenker, Martin Hägeli and
Martin Brändli for the fruitful discussions and leadership that made this research
possible. This research has been funded and conducted in cooperation with the Swiss
Federal Office for the Environment (FOEN). Related research was funded by the
European Commission and by the Swiss Federal Office for Education and Science
within the 6th-Framework Programme project REWERSE number-506779 (cf.
http://rewerse.net).
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