Querying Linked Geospatial Data with Incomplete InformationC. Nikolaou0M. Koubarakis0Department of Informatics and Telecommunications National and Kapodistrian University of Athens
,
Greece
Linked geospatial data has recently received attention, as researchers and practitioners have started tapping the wealth of geospatial information available on the Web. Incomplete geospatial information, although appearing often in the applications captured by such datasets, is not represented and queried properly due to the lack of appropriate data models and query languages. We discuss our recent work on the model RDFi, an extension of RDF with the ability to represent property values that exist, but are unknown or partially known, using constraints, and an extension of the query language SPARQL with qualitative and quantitative geospatial querying capabilities. We demonstrate the usefulness of RDFi in geospatial Semantic Web applications by giving examples and comparing the modeling capabilities of RDFi with the ones of related Semantic Web systems.
linked geospatial dataincomplete informationRDF-
Linked data is a new research area which studies how one can make RDF data
available on the Web, and interconnect it with other data with the aim of
increasing its value for everybody [
4
]. The resulting \Web of data" has recently
started being populated with geospatial data. A representative example of such
e orts is LinkedGeoData1 where OpenStreetMap data is made available as RDF
and queried using the declarative query language SPARQL [
2
]. With the recent
emphasis on open government data, some of it encoded already in RDF2,
portals such as LinkedGeoData demonstrate that the development of useful Web
applications might be just a few SPARQL queries away. The recent paper [
9
] by
our group addresses many research topics and relevant questions that deserve
the attention of researchers in the area of linked geospatial data.
In the context of the research agenda presented in [
9
], we have developed
stSPARQL [
17
], an extension of the query language SPARQL for querying linked
1 http://linkedgeodata.org/
2 http://data.gov.uk/linked-data/
geospatial data. The geospatial component of stSPARQL has been fully
implemented in our open source system Strabon3 which also supports GeoSPARQL,
the recent proposed standard by OGC (Open Geospatial Consortium) for
querying geospatial data expressed in RDF. Strabon is currently being used to query
linked data describing sensors in the context of project SemsorGrid4Env4 [
16
]
and linked earth observation (EO) data in the context of project TELEIOS5 [
12
].
A signi cant aspect of querying linked geospatial data that has not been
addressed yet is querying linked geospatial data with incomplete information [
11
].
Incomplete information, although appearing often in applications captured by
such datasets, is not represented or queried properly due to the lack of
appropriate data models and query languages. For example, a wild re monitoring and
management application, developed by us in TELEIOS, requires the integration
of multiple, heterogeneous data sources, some of them available on the Web,
with data of varying quality and varying temporal and spatial scales. As a
result, incomplete information needs to be represented in stRDF and queried by
stSPARQL.
In this paper we address the problem of representing and querying incomplete
geospatial information in RDF using the RDFi framework that we have recently
developed in [
19
]. RDFi is a framework that extends RDF with the ability to
represent property values that exist, but are unknown or partially known, using
constraints. RDFi is a general framework for the representation of incomplete
information of this kind and it can be employed in various application domains,
such as temporal and spatial. In this paper, we concentrate on the spatial
domain only and demonstrate the modeling capabilities of RDFi and the querying
capabilities of our extension of SPARQL which is based on stSPARQL.
The organization of the paper is as follows. Section 2 introduces the RDFi
framework. Section 3 describes the kinds of linked geospatial data that we need
to represent in the wild re monitoring application of TELEIOS. Then, Section 4
demonstrates the RDFi framework giving examples motivated from that
application of TELEIOS. Finally, Section 5 compares the expressive power of RDFi
with related semantic web systems, while Section 6 concludes our work.
The paper is mostly informal and uses examples from the wild re monitoring
application of TELEIOS. Even in the places where the paper becomes formal,
we do not give any detailed technical results for which the interested reader is
directed to [
13, 14, 19
] and the survey paper [
9
].
2
The RDFi framework
The RDFi framework developed by us in [
19
] (where \i" stands for
\incomplete") is an extension of the RDF framework addressing an important kind
of incomplete information that has so far been ignored in the context of RDF;
3 http://www.strabon.di.uoa.gr/
4 http://www.semsorgrid4env.eu/
5 http://www.earthobservatory.eu/
representation of values that exist but are unknown or partially known. RDFi
extends RDF with the ability to de ne a new kind of literals for each datatype.
These literals are called e-literals (\e" comes from the word \existential") and
can be used to represent values of properties that exist but are unknown or
partially known. Such information is abundant in recent applications where RDF is
being used (e.g., sensor networks, the modeling of geospatial information, etc.).
In RDFi, e-literals are allowed to appear only in the object position of triples.
Previous research on incomplete information in databases and knowledge
representation has shown that in many applications, having the ability to state
constraints about values that are partially known is a very desirable feature and
leads to the development of very expressive formalisms [
5, 8
]. In the spirit of this
tradition, RDFi allows partial information regarding property values represented
by e-literals to be expressed by a quanti er-free formula of a rst-order constraint
language L. Thus, RDFi extends the concept of an RDF graph to the concept
of an RDFi database which is a pair (G; ) where G is an RDF graph possibly
containing triples with e-literals in their object positions, and is a quanti
erfree formula of L.
The semantics for RDFi databases and SPARQL query evaluation has been
de ned following ideas from the incomplete information literature [
5, 6
]. The
semantics de nes the set of possible RDF graphs corresponding to an RDFi
database and the fundamental concept of certain answer for SPARQL query
evaluation over an RDFi database.
The well-known concept of representation system from the seminal paper
of [
6
] has been transferred to the case of RDFi. It has been shown in [
19
] that
CONSTRUCT queries without blank nodes in their templates and using only
the operators AND, UNION, and FILTER or the restricted fragment of graph
patterns corresponding to the well-designed patterns of [
1
] can be used to de ne
a representation system for RDFi. Last, [
19
] de nes the fundamental concept
of certain answer to SPARQL queries over RDFi databases and presents an
algorithm for its computation.
3
Linked geospatial data in the wild re monitoring application of TELEIOS
The wild re monitoring application of TELEIOS concentrates on the
development of solutions for real time hotspot and active re front detection, and burnt
area mapping. Technological solutions to both of these cases require integration
of multiple, heterogeneous data sources with data of varying quality and varying
temporal and spatial scales. Some of the data sources are streams (e.g., streams
of EO images) while others are static geo-information layers (e.g., land use/land
cover maps) providing additional evidence on the underlying characteristics of
the a ected area.
In what follows, we brie y describe some of the datasets used by the National
Observatory of Athens (NOA) that is leading the wild re monitoring application
of TELEIOS.
Hotspot maps. NOA operates a MSG/SEVIRI6 acquisition station and
receives raw satellite images every 15 minutes. These images are processed using
image processing algorithms to detect the existence of hotspots. Information
related to hotspots is stored in ESRI shape les and KML les. These les hold
information about the date and time of image acquisition, cartographic X, Y
coordinates of detected re locations, the level of reliability in the observations, the
re radiative power assessed, and the observed re area. NOA receives similar
hotspot shape les covering the geographical area of Greece from the European
project SAFER (Services and Applications for Emergency Response).
Burnt area maps. From project SAFER, NOA also receives ready-to-use
accumulated burnt area mapping products in polygon format, projected to the
EGSA87 reference system7. These products are derived daily using the MODIS
satellite and cover the entire Greek territory. The data formats are ESRI
shapeles and KML les with information relating to date and time of image
acquisition, and the mapped re area.
Corine Land Cover data. The Corine Land Cover project is an activity
of the European Environment Agency which is collecting data regarding land
cover (e.g., farmland, forest) of European countries. The Corine Land Cover
nomenclature uses a hierarchical scheme with three levels to describe land cover:
{ The rst level consists of ve items and indicates the major categories of
land cover on the planet, e.g., forests and semi-natural areas.
{ The second level consists of fteen items and is intended for use on scales of
1:500,000 and 1:1,000,000 identifying more speci c types of land cover, e.g.,
open spaces with little or no vegetation.
{ The third level consists of forty-four items and is intended for use on a
scale of 1:100,000, narrowing down the land use to a very speci c geographic
characterization, e.g., burnt areas.
The land cover of Greece is available as an ESRI shape le that is based on the
Corine Land Cover nomenclature.
Coastline geometry of Greece. An ESRI shape le that describes the
geometry of the coastline of Greece is available.
In [
15, 17
] we discuss in great detail how we can query linked geospatial data
such as the above using the model stRDF and the query language stSPARQL. In
this work we concentrate on the representation and querying of linked
geospatial data with incomplete information. This is presented in the following
section by giving examples motivated from the wild re monitoring application of
TELEIOS.
6 MSG refers to Meteosat Second Generation satellites, and SEVIRI is the instrument
which is responsible for taking infrared images of the earth.
7 EGSA87 is a 2-dimensional projected coordinate reference system that describes the
area of Greece.
Incomplete geospatial information in the wild re monitoring application of TELEIOS
This section motivates our approach towards extending RDF with the ability to
represent and query incomplete information.
As mentioned in Section 3, NOA receives satellite images for the entire Greek
re season on a 15-minute basis from the SEVIRI infrared imager of a Meteosat
Second Generation satellite. After the images are processed for georeferencing,
they are analyzed by specialized image processing software to detect hotspots
(i.e., regions of the image corresponding to geographic regions that are probably
on re). Processing of images results in the generation of shape les representing
hotspots as point-vectors.
The following is a list of triples (namespaces are omitted) that gives an
example of the kind of representation that is currently used by NOA for representing
these hotspots and making them available as linked data to relevant public
authorities.
hotspot1 type Hotspot .
fire1 type Fire .
hotspot1 correspondsTo fire1 .
fire1 occuredIn region1 .
region1 hasGeometry "x = 24:825668 ^ y = 35:310643"^^SemiLinearPointSet .
The above list of triples is a graph in the model stRDF of [
10
] which extends
RDF with the ability to represent geometries over Qk that change over time
following the paradigm of constraint databases [
7
]. In stRDF, geometries and
valid times of triples are expressed using Boolean combinations of linear
constraints that are given as literals of type SemiLinearPointSet de ned in [
10
].
Semi-linear point sets are the subsets of Qk de ned by Boolean combinations
of linear constraints. The above graph represents de nite information; it states
that there is a hotspot (hotspot1) and that the corresponding re (fire1) takes
place at the point (24:825668; 35:310643) 2 Q2.
In practice, due to the technical weaknesses of the instruments attached to
satellites and inherent distortions of the algorithms applied on satellite images for
knowledge extraction, the extracted spatial information can only be inde nite.
For example, the SEVIRI imager has medium resolution and therefore each
image pixel representing a hotspot corresponds to a 3km by 3km rectangle in
geographic space. Accordingly, NOA represents hotspots as points in geographic
space using the center of the corresponding rectangle.
In this case, another useful representation of the real world situation that
corresponds to a hotspot would be to state that there is a geographic region
with unknown exact coordinates where a re is taking place, and that region
is included in a known 3km by 3km rectangle. This real world situation can be
represented by an RDFi database as shown in the following example.
Example 1. The following is an RDFi database encoding information about a
detected hotspot.
hotspot1 type Hotspot .
fire1 type Fire .
hotspot1 correspondsTo fire1 .
fire1 occuredIn _R1 .
R1 NTPP "x
6 ^ x
Fire fire1 (red area of Figure 1) is asserted to have taken place inside region
R1. R1 is an e-literal of datatype SemiLinearPointSet and is asserted to
be inside the rectangle formed by the points (6; 8) and (23; 19) (rectangle P
of Figure 1)8. This is stated with a constraint expressed in the language PCL
(Polygon Constraint Language), a rst-order constraint language that allows us
to represent topological properties for polygons. NTPP is the
\non-tangentialproper-part" relation of RCC-8 [
24
]. In general, constraints in PCL can be used
to express qualitative and quantitative spatial information about regions in Q2.
The example shows that e-literals are like existentially quanti ed variables in
rst-order logic or Skolem constants. E-literals can be used to represent values of
properties that exist but are unknown or partially known (e.g., by constraining
the value of an e-literal).
RDFi databases like the one of Example 1 consist of two parts: a graph (i.e.,
a set of triples) and a global constraint. Global constraints can in general be
quanti er-free formulae of some rst-order constraint language. RDFi databases
are syntactic devices for the representation of incomplete information. An RDFi
database is semantically equivalent to a set of possible RDF graphs that represent
all the possible ways the domain of application could have been according to our
incomplete information. One can nd all the possible RDF graphs represented
by an RDFi database as follows: a) nd an assignment to e-literals that satis es
the global constraint and b) substitute these values for the e-literals in the RDFi
database.
8 For sake of readability of the examples, we chose to use small, integer numbers
instead of real geographic coordinates.
For example, the RDF graph shown below is one of the possible RDF graphs
corresponding to the RDFi database of Example 1.
hotspot1 type Hotspot .
fire1 type Fire .
hotspot1 correspondsTo fire1 .
fire1 occuredIn "x 10 ^ x 21 ^ y
Example 2. Let us consider the query \Find all res that have occurred in a
region which is a non-tangential proper part of rectangle Q1 of Figure 1" over
the database of Example 1. In the extension of SPARQL we consider, this query
can be expressed as follows:
SELECT ?FWHERE {
}
The version of SPARQL we consider extends FILTER expressions of standard
SPARQL [
23
] allowing also expressions of a rst-order constraint language, such
as PCL, for constraining the values of spatial variables. These expressions have a
functional-like syntax and are interpreted in the underlying rst-order language.
For example, the global constraint of the RDFi database of Example 1 would be
speci ed in a FILTER expression as
NTPP(?R, "x
6 ^ x
to constrain the value of the spatial variable ?R.
What is the answer to the query of Example 2? If we examine the database
of Example 1 (Figure 1), we can see that the answer should be conditional [
6
].
We cannot say for sure whether fire1 satis es the requirements of the query
because the information in the database is inde nite (the exact geometry of R1
is not known). Fire fire1 quali es only in the possible graphs where R1 is a
non-tangential proper part of the rectangle mentioned in the query. For every
object that quali es as an answer, the query answering procedure should also
provide a condition characterizing this set of possible graphs. Following the ideas
of conditional tables from [
6
], this answer can be represented by the following
set of conditional mappings (see [
19
] for a formal de nition):
?F Condition
fire1 R1 NTPP "x
Conditional mappings are di erent from standard SPARQL mappings [
22
] in
the sense that they map variables to constants only if a condition holds. Thus,
they are reminiscent of conditional tuples in the conditional table model of [
5
].
In RDFi, the basic concept of triple is also de ned to be conditional.
Example 3. If we wanted to have an RDFi database as the answer to a query
like the one of Example 2, then we would have queried the RDFi database of
Example 1 using the CONSTRUCT query form of SPARQL as follows:
CONSTRUCT { ?F type Fire }WHERE {
The answer to this query would be an RDFi database containing conditional
triples adhering to the query template (i.e., f?F type Fireg). The template
is instantiated for each conditional mapping from the evaluation of the graph
pattern of the query, and the resulting triple together with the condition of
the mapping form a conditional triple in the resulting database. Therefore, the
answer to query of Example 3 consists of the following conditional triple:
fire1 type Fire [ R1 NTPP "x
In some cases the user might know that the information in the database is
incomplete. Thus, she might wish to nd all values that certainly satisfy some
quali cation. This is the well-known notion of certain answer in the incomplete
databases literature [
5
] and it is demonstrated in the following example.
Example 4. Let us consider the query of Example 3 again and rephrase it to
\Find res that have certainly occurred in a region which is a non-tangential
proper part of rectangle Q2 of Figure 1". In the version of SPARQL we consider,
this query would be expressed as follows:
Inspecting Figure 1, it is obvious that fire1 satis es the query unconditionally.
Hence, the certain answer contains the following RDF triple
fire1 type Fire .
CERTAIN CONSTRUCT { ?F type Fire }WHERE {
?F type Fire .
?F occuredIn ?R .
FILTER ( NTPP(?R, "x
2 ^ x
28 ^ y
4 ^ y
22") )
In contrast to Example 3 where the answer to the CONSTRUCT query
is an RDFi database, the answer to a CONSTRUCT query with a CERTAIN
operator, like the one of Example 4 above, is an RDF graph. This is anticipated
since a certain answer can not contain conditional information.
5
i
Expressive power of RDF : An informal comparison
In this paper we gave examples of the use of RDFi in geospatial applications.
Thus, it would be interesting to compare the expressive power that RDFi gives
us to other recent works that use Semantic Web data models and languages for
geospatial applications.
When equipped with a constraint language like PCL (or TCL9) [
19
], RDFi
goes beyond the proposals of [
10, 17
] and [
20
] that cannot express incomplete
geospatial information. Incomplete geospatial information as it is studied in this
paper can also be expressed in spatial description logics [
18, 21
]. For e ciency
reasons, spatial DL reasoners such as RacerPro10 and PelletSpatial11 have opted
for separating spatial relations from standard DL axioms as we have done by
separating graphs and constraints. Since RDF graphs can be seen as DL ABoxes
with atomic concepts only, all the results of this paper can be trivially transferred
to the relevant subsets of spatial DLs and their reasoners.
In the following we concentrate on the reasoner PelletSpatial since it is a
more recent proposal than RacerPro and discuss how RDFi is related to the
recently proposed Semantic Web technologies of [
3, 26
].
PelletSpatial [
25
] is a hybrid spatial reasoner that provides RCC-8 and OWL
2 reasoning and querying capabilities. In PelletSpatial, spatial relations are
separated from OWL 2 relations providing a hybrid reasoner for both spatial and
thematic data. Spatial relations are managed as an RCC-8 constraint network.
Conjunctive query answering in PelletSpatial requires two phases: a) evaluating
spatial query atoms over the constraint network by employing a path-consistency
algorithm, and b) further constraining the set of bindings such that the
nonspatial query atoms are satis ed.
Compared to the RDFi framework, PelletSpatial corresponds to RDFi
databases with a conjunction of TCL-constraints as a global constraint. Compared
to our extension of SPARQL, the query language of PelletSpatial computes
certain answers for SPARQL queries using only the operators AND and FILTER
with conjunctions of TCL-constraints allowed as expressions in FILTER graph
patterns. The representational and querying power of RDFi when L is PCL is
greater than the one of PelletSpatial since PCL is a language more expressive
than TCL. However, PelletSpatial o ers OWL representation and reasoning that
is not o ered by RDFi.
9 TCL is like PCL but without constants, that is, TCL can express topological
constraints only between variables.
10 http://www.racer-systems.com/
11 http://clarkparsia.com/pellet/spatial/
A more general and formal approach to modeling spatial information is [
26
]
that proposes an abstracted graph-based data model and query language with
which any subset of rst-order predicate logic (FOPL) (e.g., modal, description
logic) can be associated. For the case of spatial information, a substrate can play
the role of a geometric substrate, called SBox. SBox deals with spatial datatypes
(e.g., polygons) the geometry of which can be described using an appropriate
FOPL, inheriting also its formal semantics for satis ability, entailment, etc. The
authors investigate four options for representing and querying spatial
information: use (i) an ABox, (ii) a map substrate, (iii) a spatial ABox, (iv) an ABox
and RCC substrate.
Finally, [
3
] proposes SOWL, an extension of OWL, to represent spatial
qualitative and quantitative information employing the RCC-8 topological relations,
cardinal direction relations, and distance relations. To reason about spatial
relations, a set of SWRL rules are implemented in the Pellet reasoner.
6
Conclusions
This work stressed the inability of semantic web data models and query
languages to manage linked geospatial data with incomplete information. Motivated
by a real application in which representation and querying of incomplete
information is inherent, it demonstrated through the use of many examples how the
RDFi framework and an extension of the query language SPARQL [
19
] can be
employed for active re front detection and burnt area mapping in the context
of the EU project TELEIOS.
Acknowledgments
This work has been funded by the FP7 project TELEIOS (257662).
1.
M.Arenas
and
J.Perez
.
Querying semantic web data with SPARQL
.
In PODS
, pages
305
{
316
,
2011
.
2.
S.Auer
,
J.Lehmann
, and
S.Hellmann
. Linkedgeodata:
Adding a spatial dimension to the web of data
.
In ISWC'09
, pages
731
{
746
,
2009
.
3.
S.Batsakis
and
E. Petrakis.SOWL: spatio-temporal representation, reasoning and querying over the semantic web
.
In I-SEMANTICS
,
2010
.
4.
C.Bizer
,
T.Heath
, and
T.Berners-Lee
.
Linked data-the story so far
.
Int. J. Semantic Web Inf. Syst.
,
5
(
3
):1{
22
,
2009
.
5.
G.Grahne
.
The Problem of Incomplete Information in Relational Databases
, volume
554of LNCS
. Springer Verlag,
1991
.
6.
T.Imielinski
and
W.Lipski
.
Incomplete Information in Relational Databases. JACM
,
31
(
4
):
761
{
791
,
1984
.
7.
P. C.Kanellakis
,
G. M.Kuper
, and
P. Z.Revesz
.
Constraint Query Languages
.
In PODS
, pages
299
{
313
,
1990
.
8.
M.Koubarakis
.
Database models for in nite and inde nite temporal information
.
Inf
. Syst.,
19
(
2
):
141
{
173
,
1994
.
9.
M.Koubarakis
,
M.Karpathiotakis
,
K.Kyzirakos
,
C.Nikolaou
, and
M.Sioutis
.
Data Models and Query Languages for Linked Geospatial Data
. In T. Eiter and T. Krennwallner, editors,
Reasoning Web. Semantic Technologies for Advanced Query Answering
, volume
7487
of Lecture Notes in Computer Science, pages
290
{
328
. Springer Berlin / Heidelberg,
2012
.
10.
M.Koubarakis
and
K.Kyzirakos
.
Modeling and querying metadata in the semantic sensor web: The model stRDF and the query language stSPARQL
.
In ESWC
,
2010
.
11.
M. Koubarakis
,
K.Kyzirakos
,
M.Karpathiotakis
,
C.Nikolaou
,
M.Sioutis
,
S.Vassos
,
D.Michail
, T. t. Herekakis,
C.Kontoes
,
and I.Papoutsis
.
Challenges for Qualitative Spatial Reasoning in Linked Geospatial Data
.
In Proceedings of IJCAI 2011 Workshop on Benchmarks and Applications of Spatial Reasoning
,
2011
.
12.
M. Koubarakis
,
K.Kyzirakos
,
M.Karpathiotakis
,
C.Nikolaou
,
S.Vassos
, G. Garbis,
M.Sioutis
,
K.Bereta
,
D.Michail
,
C.Kontoes
, I. Papoutsis,
T.Herekakis
,
S.Manegold
,
M.Kersten
,
M.Ivanova
,
H.Pirk
,
Y.Zhang
, M. Datcu, G. Schwarz,
C.Dumitru
,
D. E.Molina
,
K.Molch
, U. D.
Giammatteo
,
M.Sagona
,
S.Perelli
,
T.Reitz
, E. Klien, and
R.Gregor
.
TELEIOS: A Database-Powered Virtual Earth Observatory
.
PVLDB
,
5
(
12
):
2010
{
2013
,
2012
.
13.
M. Koubarakis
,
C.Nikolaou
, and
V.Fisikopoulos
.
Theoretical results on query processing for RDF/SPARQL with time and space
.
Del. 2
.3,
TELEIOS
,
2011
.
14.
M. Koubarakis
et al.
A data model and query language for an extension of RDF with time and space
.
Del. 2
.1, TELEIOS project,
2011
.
15.
K.Kyzirakos
,
M.Karpathiotakis
, G. Garbis,
C.Nikolaou
,
K.Bereta
,
M.Sioutis
, I. Papoutsis,
T.Herekakis
,
D.Michail
,
M.Koubarakis
, and
H.Kontoes
.
Real Time Fire Monitoring Using Semantic Web and Linked Data Technologies
.
In ISWC'12
,
2012
.
16.
K.Kyzirakos
,
M.Karpathiotakis
, and
M.Koubarakis
.
Developing Registries for the Semantic Sensor Web using stRDF and stSPARQL
.
In SSN
, volume
668
,
2010
.
17.
K.Kyzirakos
,
M.Karpathiotakis
, and
M.Koubarakis
.
Strabon: A Semantic Geospatial DBMS
.
In ISWC'12
,
2012
.
18.
C.Lutz
and
M.Milicic
.
A tableau algorithm for description logics with concrete domains and general tboxes
.
J. Autom. Reason.
,
38
:
227
{
259
,
April2007
.
19.
C.Nikolaou
and
M.Koubarakis
.
Incomplete Information in the Semantic Web. 2012 (submitted to a conference).
20. Open Geospatial Consortium Inc.
GeoSPARQL - A geographic query language for RDF data
.
OGC
,
2010
.
21.
O. L. Ozcep
and
R.Moller. Combining DL-Lite with Spatial Calculi for Feasible Geo-thematic Query Answering
. In Description Logics,
2012
.
22.
J. Perez
,
M.Arenas
, and
C.Gutierrez
.
Semantics and complexity of SPARQL
.
ACM Trans. Database Syst
.,
34
(
3
):1{
45
,
2009
.
23. E.
Prud'hommeaux andA.Seaborne. SPARQL QueryLanguage for RDF
.
W3C Recommendation 15 Jan
.
2008
.
24.
D. A.Randell
,
Z.Cui
,
andA. G.Cohn
.
A spatial logic based on regions and connection
.
In KR
, pages
165
{
176
,
1992
.
25.
M.Stocker
and
E. Sirin.PelletSpatial: A hybrid RCC-8 and RDF/OWL reasoning and query engine
.
In OWLED
,
2009
.
26.
M.Wessel
and
R.Moller
.
Flexible software architectures for ontology-based information systems
.
JAL
,
7
(
1
):
75
{
99
,
2009
.