Implementation of mappings between the description logic and the binary relational data model on the RDF level
This paper is dedicated to the data integration problem. In article the task of practical implementation of mappings between description logic and a binary relational data model is discussed. This method was formulated earlier at a theoretical level. A practical technique to test mapping engines usi...
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pp_isofts_kiev_ua-article-4382024-04-26T22:46:30Z Implementation of mappings between the description logic and the binary relational data model on the RDF level Реалізація відображень між дескриптивною логікою та бінарною реляційною моделлю даних на рівні RDF Chystiakova, I.S. binary relational data model; description logic; mapping; RDF; DL; RM2; ALC; OWL UDC 004.62 бінарна реляційна модель даних; дескриптивна логіка; відображення; RDF; DL; RM2; ALC; OWL УДК 004.62 This paper is dedicated to the data integration problem. In article the task of practical implementation of mappings between description logic and a binary relational data model is discussed. This method was formulated earlier at a theoretical level. A practical technique to test mapping engines using RDF is provided in the current paper. To transform the constructs of the description logic ALC and its main extensions into RDF triplets the OWL 2-to-RDF mappings are used. To convert RDB to RDF graph, the R2R Mapping Language (R2R ML) was chosen. The mappings DL ALC and its main extensions to the RDF triplets are described in the publication. The mapping of the DL axioms into an RDF triplet also is considered in the publication. The main difficulties in describing DL-to-RDF transformations are given in the corresponding section. For each constructor of concepts and roles a corresponding expression in OWL 2 and its mapping into the RDF triplet. A schematic representation of the resulting RDF graph for each mapping is created. The paper also provides an overview of existing methods that relate to the use of RDF when mapping RDB to ontology and vice versa.Prombles in programming 2020; 4: 41-54 Ця публікація присвячена проблемі інтеграції даних, а саме – створенню механізму відображень між дескриптивною логікою та бінарною реляційною моделлю даних. Метод створення відображень був запропонований та описаний на теоретичному рівні. З метою його практичної перевірки, у поточній публікації пропонується метод реалізації відображень між дескриптивною логікою та бінарною реляційною моделлю даних за допомогою RDF. У роботі наведено огляд існуючих методів та засобів перетворення реляційних баз даних в онтологію та навпаки за допомогою RDF. Було сформульовано постановку задачі реалізації відображень та розглянуто відображення дескриптивної логіки ALC, її основних розширень, а також аксіоматики у RDF-трійки. У статті відзначено ряд складнощів при відображенні дескриптивної логіки на рівень RDF.Prombles in programming 2020; 4: 41-54 Інститут програмних систем НАН України 2021-01-25 Article Article application/pdf https://pp.isofts.kiev.ua/index.php/ojs1/article/view/438 10.15407/pp2020.04.041 PROBLEMS IN PROGRAMMING; No 4 (2020); 41-54 ПРОБЛЕМЫ ПРОГРАММИРОВАНИЯ; No 4 (2020); 41-54 ПРОБЛЕМИ ПРОГРАМУВАННЯ; No 4 (2020); 41-54 1727-4907 10.15407/pp2020.04 en https://pp.isofts.kiev.ua/index.php/ojs1/article/view/438/442 Copyright (c) 2021 PROBLEMS IN PROGRAMMING |
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binary relational data model description logic mapping RDF DL RM2 ALC OWL UDC 004.62 |
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binary relational data model description logic mapping RDF DL RM2 ALC OWL UDC 004.62 Chystiakova, I.S. Implementation of mappings between the description logic and the binary relational data model on the RDF level |
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binary relational data model description logic mapping RDF DL RM2 ALC OWL UDC 004.62 бінарна реляційна модель даних дескриптивна логіка відображення RDF DL RM2 ALC OWL УДК 004.62 |
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Implementation of mappings between the description logic and the binary relational data model on the RDF level |
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Implementation of mappings between the description logic and the binary relational data model on the RDF level |
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Implementation of mappings between the description logic and the binary relational data model on the RDF level |
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Implementation of mappings between the description logic and the binary relational data model on the RDF level |
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Implementation of mappings between the description logic and the binary relational data model on the RDF level |
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implementation of mappings between the description logic and the binary relational data model on the rdf level |
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Реалізація відображень між дескриптивною логікою та бінарною реляційною моделлю даних на рівні RDF |
| description |
This paper is dedicated to the data integration problem. In article the task of practical implementation of mappings between description logic and a binary relational data model is discussed. This method was formulated earlier at a theoretical level. A practical technique to test mapping engines using RDF is provided in the current paper. To transform the constructs of the description logic ALC and its main extensions into RDF triplets the OWL 2-to-RDF mappings are used. To convert RDB to RDF graph, the R2R Mapping Language (R2R ML) was chosen. The mappings DL ALC and its main extensions to the RDF triplets are described in the publication. The mapping of the DL axioms into an RDF triplet also is considered in the publication. The main difficulties in describing DL-to-RDF transformations are given in the corresponding section. For each constructor of concepts and roles a corresponding expression in OWL 2 and its mapping into the RDF triplet. A schematic representation of the resulting RDF graph for each mapping is created. The paper also provides an overview of existing methods that relate to the use of RDF when mapping RDB to ontology and vice versa.Prombles in programming 2020; 4: 41-54 |
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Інститут програмних систем НАН України |
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2021 |
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https://pp.isofts.kiev.ua/index.php/ojs1/article/view/438 |
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| fulltext |
Моделі та засоби систем баз даних і знань
© I.S. Chystiakova, 2020
ISSN 1727-4907. Проблеми програмування. 2020. № 4 41
UDC 004.62 https://doi.org/10.15407/pp2020.04.041
I.S. Chystiakova
IMPLEMENTATION OF MAPPINGS BETWEEN THE
DESCRIPTION LOGIC AND THE BINARY RELATIONAL DATA
MODEL ON THE RDF LEVEL
This paper is dedicated to the data integration problem. In article the task of practical implementation of
mappings between description logic and a binary relational data model is discussed. This method was for-
mulated earlier at a theoretical level. A practical technique to test mapping engines using RDF is provided in
the current paper. The mappings DL ALC and its main extensions to the RDF triplets are described in the
publication. The mapping of the DL axioms into an RDF triplet also is considered in the publication. The
main difficulties in describing DL-to-RDF transformations are given in the corresponding section. The paper
also provides an overview of existing methods that relate to the use of RDF when mapping RDB to ontology
and vice versa.
Key words: binary relational data model, description logic, mapping, RDF, DL, RM
2
, ALC, OWL.
Introduction
The research series [1–7] is dedicated
to the analysis and solution of the problem of
creating a mapping mechanism between the
description logic (DL) and the relational data
model (RDM). It took place as a part of the
complex problem of data integration, the
analysis of which can be found in [7]. The
mentioned series provides an overview of the
current existing approaches to address the
problem of mapping. According to the result
of analysis a taxonomy of research on the
subject was created. This result also revealed
a number of disadvantages of the existing
approaches to establish one-to-one corre-
spondences between the description logic
and the relational data model. Based on this
a binary relational data model (RM
2
) was
proposed as an integrating model for the cre-
ation of mappings. Complete and detailed
description of it can be found in [1]. Infor-
mation about the interaction between RM
2
and the classical relational data model can be
found in [2].
The mechanism for mapping the ALC
description logic and its main extensions to
RM
2
was developed and described in [6], as
well as classical RDM to RM
2
. In the publica-
tion [6] you can get acquainted with the ar-
gumentation of the following statement: de-
scription logic can be considered as an inde-
pendent data model. It also describes in detail
why DL ALC is used in the developed ap-
proach, justifies the choice of ALC extensions
and outlines the way they are mapped in RM
2
.
Until now a significant drawback of
this approach has been the lack of any practi-
cal testing of the proposed results. The de-
scription of mappings using RM
2
is purely
theoretical. A real practical check can make
significant changes both in the structure of the
approach itself and in its main individual
components, e.g. to complement or restrict the
operations of a binary relational algebra
(RA
2
), which is a constituent part of RM
2
. In
the current paper a method for checking map-
pings between the description logic and the
binary relational data model using RDF
graphs is proposed.
Section 1 is dedicated to the analysis
of the number of practical works on the im-
plementation of mappings using RDF. Section
2 formulates the problem of practical appro-
bation of the approach to the description of
mappings between DL and RDM. Section 3
outlines a method for mapping the description
logic ALC and its extensions to RDF using
OWL 2. Conclusions can be found in the
section 4.
Related work
The publications [1, 6] provide an
overview of the current approaches to address
the problem of mapping. According to the re-
sult of analysis a taxonomy of research on the
subject was created. It is shown in Fig. 1.
Моделі та засоби систем баз даних і знань
42
The results given in [1, 6] will not be
duplicated in the current paper. On the contra-
ry, this section is dedicated to works that were
not included in the above survey. The publi-
cations that will be overviewed in this part of
the article are intended to complement the
existing taxonomy. They will be classified
and will take their place in the hierarchy of
the body of research on the establishment of
correspondences between ontologies and rela-
tional databases. This overview focuses on
those methods that concern the use of RDF at
RDB-to-ontology mapping or ontology-to-
RDB mapping. There is a need to allocate a
place in the corresponding column of the tax-
onomy for the researches that will be consid-
ered in the current section. Also, it is neces-
sary to formulate a number of intermediate
conclusions that are necessary for setting the
task of a current work.
Fig. 1. The approaches to describe mappings
between DL and RDB research taxonomy
The first step is to consider the fun-
damental work [8]. It belongs to the following
section of the classification: direct mapping of
RDB in ontology, the direction is mappings
taking into account the analysis of RDB data.
It should be noted the following features of
this study:
1. A clear distinction between the
concepts of "mapping RDB into ontology"
and "transformation of RDB into ontology". If
in the first case interaction between the exist-
ing ontology and the database is supposed,
then in the other case it is supposed to create a
completely new ontology based on the data
and the RDM structure. The authors of the
approach attribute it to the second case.
2. Using RDF in the transformation
rules. A large amount of literature provides a
set of rules that map RDB constructs directly
into the ontology construct, without using an
intermediate model [8]. Such an ontology is
built as a result of a direct transformation
from a semantically less developed database.
It suffers from a number of serious short-
comings, which are mentioned by the authors
of study. The difference of this approach
from the others is that an independent at-
tempt to transform the RDB structure and
data into an OWL structure that is built with
the help of RDF and RDFS using XSD is
made. The database data is converted into
regular RDF triples.
In fact, this is one of the first serious
studies in the field of establishing interoper-
ability between ontologies and RDB using
RDF. The authors of the methodology do not
use the R2R ML language, which has the
official W3C specification. However, in the
section dedicated to the source analysis the
existence of various approaches that use both
RDF-OWL constructs and those using
R2R ML is mentioned. The R2R ML itself
will be discussed below.
This approach has a serious draw-
back: there is no mention of how the opera-
tions of relational algebra are mapped. In
their continued research [9], the authors of
the technique tried to eliminate it. Based on
the rules for transforming the structural part
of the database and its data, the rules for
mapping the relational algebra operators (ex-
pressed in SQL) into equivalent SPARQL
queries were made. If we consider this ap-
proach in a complex of two works [8, 9],
then it can be retrained and referred to the
taxonomy section as the direct mapping of
RDB in ontology, the direction is mappings,
taking into account the analysis of queries to
the RDB.
Generally, this approach does not
stand out from the general mass of other
methods in its category. It has the same
drawbacks: the one-sidedness of the mecha-
nism (although the authors note that the de-
scription of the mapping rules in the opposite
direction remains in the field of future re-
search), the absence of a formal approach,
the separation of the structural and manipula-
R
es
ea
rc
h
d
ir
ec
ti
o
n
s
Using an intermediate RDB
Direct mapping of ontology
to RDB
Direct mapping of RDB to
ontology
Mapping RDB metadata to
ontology
Mappings based on the
analysis of RDB data
Mappings based on the
analysis of queries to the
RDB
Creation and use of an
ontology-oriented RDB
Моделі та засоби систем баз даних і знань
43
tive parts of the RDB within a unified ap-
proach, as well as the silence that ontologies
and RDB obeys two different open and
closed world hypotheses. It remains unclear
how the interaction between these two very
different concepts will be
carried out.
It should be mentioned that in studies
dedicated to the mappings subject matter, a
number of works that present their specifica-
tion of mapping languages have appeared.
For example, in [10, 11] the RDB2OWL
Mapping Language specification is declared,
where the specification and tools for map-
ping implementation are presented. Howev-
er, despite the deep study of the topic and the
presence of serious practical testing,
RDB2OWL ML operates exclusively with
the structural part of RDM. The approach
pays attention to the aspect of integrity con-
straints but does not address the relational
algebra operations converting.
Analyzing the works dedicated to the
practical implementation of mappings, there
was revealed the following tendency: many
successful techniques increasingly prefer to
work not directly with OWL, but using RDF
and RDFS, in conjunction with XML data
types. There are the following reasons for
this. Over the years the W3C has released
two official specifications for mapping
mechanisms between OWL, RDF, and RDB.
One of them [12] describes the mapping
mechanism of the OWL ontology into an
RDF triplet. The document provides an ex-
haustive list of rules for transforming each
OWL construct into a set of RDF triplets. It
also contains a description of the mechanism
for transforming RDF triplets into the corre-
sponding OWL constructs, with the neces-
sary list of transformation rules. Another
document [13] declares the R2R ML (RDB
to RDF Mapping Language) language speci-
fication, which describes the mechanism for
mapping a relational database to the set of
RDF triplets. Thus, RDF is established by
default as the intermediate stage in mappings
between DL and RDM.
This is argued as follows.
1. Looking at the semantic web pie's
stack architecture, it is seen that OWL and
RDF are adjacent layers. That is, a very im-
portant task is to show the way of interaction
between two parts of the same concept.
2. Accessing data from the “deep
web”. This term refers to data that is very
difficult to index with standard search en-
gines. These include, for example, unstruc-
tured documents (pictures, scanned copies),
semi-structured (CSV, PDF files), structured
data sources (RDB, XML databases, NoSQL
databases, LDAP directories). However, to
ensure the sustainability of the applications
that were developed along with the data they
exploit, and to leverage the properties engi-
neered into RDBs for decades (scalability,
ACID properties, security, performance opti-
mization), the data should remain hosted and
delivered by the legacy RDBs. This situation
creates a need for RDB-to-RDF methods that
can access relational data and convert it into
RDF triplets.
3. Linked data. Linking open data to
other related pieces of data increases its value.
Driven by recommendations proposed by Tim
Berners-Lee [14] the Linking Open Data
community project aims at extending today`s
web by publishing various open data sets in
the RDF model and setting RDF links be-
tween data sources. This is done in order to
enable developers of new programs and ap-
plications to use existing data in a new ca-
pacity, i.e. create added value by repurposing
datasets, using the data in some new way,
possibly beyond what data providers may
have initially expected.
4. Integration of heterogeneous
sources. This point has been discussed several
times earlier. However, it is worth reminding
the main aspects. In the modern web, there is
an acute problem of using not just data, but
also their semantics. Relational schemas usu-
ally convey no or poor semantics. This means
that it is necessary to define somehow the
semantics of the data stored in RDB in an
explicit machine-readable form. Using RDF
as a format for representing relational data
appears as a powerful and promising method
to achieve such data integration, in which
RDB-to-RDF methods will pay a key role.
The last three points were taken from
a fundamental review [15] of methods and
tools for converting RDB to RDF. The paper
Моделі та засоби систем баз даних і знань
44
describes similar studies that were conducted
earlier. It notes that no RDB-to-RDF research
has been conducted since the publication of
R2R ML in 2012. As a result, none of the
articles cited in the overview didn`t review
the R2R ML compliant tools.
The authors in [15] proposed the fol-
lowing classification of RDB-to-RDF re-
search areas:
- description of mappings (mapping
type, expression);
- implementation of mappings
(when and how data is converted to RDF);
- data retrieval method (query-
based methods, related data).
According to this classification, 17
approaches are ordered in the review. There is
also a separate detailed analysis of the
R2R ML language. The conclusions to the
work indicate that it is a promising language,
which, however, may not be applicable to the
entire wide range of RDB-to-RDF mapping
needs, leaving room for future research.
In this regard, in current paper for a
practical test of the implementation of map-
pings between DL and RDM, the task was
formulated: to describe a way to check map-
pings between the description logic and a bi-
nary relational data model using RDF graphs.
A detailed description of the problem state-
ment is presented in the next section.
Problem statement
Before setting the task, it is necessary
to give a brief description of the proposed
theoretical approach for mappings creation
between description logic and the relational
data model. The results of the description of
mappings DL to RM
2
can be found in [1].
Here is a summary of their essence.
The mappings DL to RM
2
can be split
into the following components:
1. To build a conceptual information
model of DL and to transform it into RM
2
.
One of the main tasks of the conceptual in-
formation model of any subject area is to de-
fine the basic concepts and to describe their
properties and relationships. The ER language
is one of the most used for this purpose. It
assumes that a conceptual information struc-
ture is described using concepts such as enti-
ty, attribute and relationship. The conceptual
information model of description logic with a
detailed description of its components can be
found in [6]. It also contains the RM
2
scheme,
which corresponds to the given ER-model.
2. To map DL ALC into RM
2
. Any de-
scription logic consists of two conceptual
parts: syntax and semantics. The latter is
specified through the interpretation concept.
Interpretation is a pair I = (Δ, •I), where Δ is a
non-empty set called the domain of interpreta-
tion and •I is an interpretation function, which
assigns to each atomic concept A a set A
I
⊆ Δ
and to each atomic role R a binary relation R
I
⊆ Δ ⨉ Δ. In turn, RDM operates with the set-
theoretical concepts of intension and exten-
sion. The establishment of such correspond-
ences between the components of the DL syn-
tax and the RM
2
intension, in which the se-
mantics of the DL expression will be equal to
the extension of the corresponding RM
2
ex-
pression will be called the mapping. The the-
oretical representation of formulas for con-
verting the DL ALC syntax into RM
2
can be
found in [6].
3. To map DL ALC extensions into
RM
2
. There are many different DL dialects.
They represent a basis of ALC logic extended
with one or more operations. For example,
DL SHOIQ denotes the presence of all ALC
syntax operators, and also includes operations
of number restrictions, nominals, and there is
also a role hierarchy, transitive and inverse
roles. More information about how to create
an ALC extensions by adding a new operation
to it can be found here [16]. Also, a detailed
description of which extensions were covered
by the theoretical research with their mapping
in RM
2
can be found in [3–5].
Based on the analysis in the previous
section, the following idea arose to test the
mapping mechanism between DL and RDM.
It is known that the mathematical basis of any
ontology describing language is description
logic. Thus, all constructors of concepts and
roles that are present in the foundational DL
are reflected in the toolbox of the correspond-
ing language. OWL 2 is no exception. It also
has the official W3C specification. Based on
Моделі та засоби систем баз даних і знань
45
this fact to set the approbation problem of the
theoretical part of the description of mappings
between DL and RDM the following idea is
proposed. Description logic statements ex-
pressed in OWL 2 are mapped to RDF triplets
using OWL-to-RDF conversion rules on the
one hand, and RDB expressions to RDF tri-
plets are mapped using R2R ML on the other
hand. The resulting graphs are compared by
equivalence criteria.
The idea of such an implementation is
schematically shown in Fig. 2.
Fig. 2. The mapping method between DL and
RM
2
checking scheme
The idea of proof is not new. The
global meaning is to transform a statement in
a new theory into statements of some other
existing theory. The next step is to prove the
statement obtained as a result of the trans-
formation within the framework of those
methods and proofs of the established con-
cept. If in the existing theory this statement
is true, then in the area being proved the cor-
related expression is also true.
In our case, there is some statement
of description logic that is mapped into a
statement of a binary relational data model.
Such a statement is represented in an
OWL 2-expression from the DL side. Further
such an expression is transformed into RDF
triplets, forming an RDF graph, using the
official W3C rules for mapping OWL-RDF.
The statement is formulated in terms of RDB
from the RM
2
side. Such a statement is then
transformed into RDF triplets using the
R2R ML language [13]. The resulting triples
constitute an RDF graph. Thus, as a result of
such transformations, two RDF graphs are
obtained. They are proposed to be compared.
If they are equivalent, then the DL-to-RM
2
mapping formula is true.
Here some points should be men-
tioned. As known [17], OWL 2 is based on
the SROIQ description logic. Thus, in the
documentation on OWL-to-RDF mapping
[12], all issues related to both the basic syn-
tax of DL ALC and the main extensions
(concepts and roles hierarchy, nominals,
number restrictions, inverse roles, DL axio-
matics, as well as some of the roles re-
strictions) are worked out in detail. However,
the scope of mapping OWL 2 to RDF is lim-
ited only by those operations that are present
in DL SROIQ. The issue of mapping some of
the role constructors in RDF, for which the
theoretical part of DL-to-RM
2
mappings has
been worked out, remains open.
The question of converting RDM
to RDF is not so simple. Obviously,
R2R ML allows you to transform the
RDB structure and integrity constraints into
RDF triplets. However, the way how to map
the manipulative part of RDM without using
the SPARQL query language have not yet
been found. A mapping method of the opera-
tions of relational algebra is currently being
investigated.
The key question of the approbation
problem is to prove the equivalence of the
resulting graphs as a result of pairwise map-
ping of statements DL and RM
2
. In the
course of research, the conclusion that an
RDF graph is a special case of an ordinary
graph was formulated. This means that the
question of equivalence is leaded to proving
their isomorphism. It was found that such a
problem has already been investigated in
[17]. It analyzes an RDF graph as a special
case. Also all isomorphism criteria for the
general case were studied. On the basis of
these criteria three necessary and sufficient
conditions for the equivalence of RDF
graphs are formulated. Let's list them:
1. Equal number of vertices. Both
graphs must contain the same number of ver-
tices. Otherwise they are not isomorphic.
2. Equivalence of vertices. In a pair-
wise comparison, each vertex of one graph
must have an equivalent in the other graph.
Otherwise, such graphs are not isomorphic.
DL RM2
RDF RDF
OWL-to-RDF R2R ML
?
Mappings
Моделі та засоби систем баз даних і знань
46
3. Equivalence edges. In a pairwise
comparison, each edge of one graph must
have an equivalent in the other graph. Other-
wise, such graphs are not isomorphic.
The last question that needs to be
worked out within the task is reducing the
graph to a self-isomorphic. As a result of
mappings, at the RDF level, a situation may
arise when the vertex of one graph will se-
mantically correspond to a subgraph from
the graph with which the comparison is
made. On the RDF level as a result of map-
pings may arise such a situation: the vertex
of one graph will semantically correspond to
a subgraph from the graph with which the
comparison is made. Such a subgraph can
consist of several vertices connected by edg-
es. This situation should be assumed as a
result of such a fact: when a statement is
mapped to RDF, a large number of anony-
mous (empty) nodes arise, which, neverthe-
less, have their own semantic purpose. Thus,
the question of reducing an RDF graph to a
self-isomorphic remains open.
Mapping DL to RDF
It is known [18] that all modern de-
scription logics are based on the simplest
version of DL ALC. This means that it is fully
included in the DL SROIQ. Therefore,
OWL 2 uses all the functionality of ALC.
The syntax for this logic is defined as
follows:
⏉ | ⏊ | A | ¬C | C ⊓ D | C ⊔ D | ∃R.C | ∀R.C,
where A – atomic concept, R – atomic role,
C, D – concept.
The concept of DL semantics does not
play a significant role in the context of map-
ping to RDF, so in this article there is no fo-
cus on this point.
The OWL 2 ontology and the mapped
graph are related as follows:
G = T(O),
where G – graph, O – ontology, T – the map-
ping function.
Before proceeding to the description
of the mappings, a number of designations
should be given. To describe OWL 2 con-
structs the OWL Abstract Syntax will be
used. To describe RDF expressions, the
standard triples and serialization to N3 nota-
tion will be used.
Table 1 shows the notation for the
main namespaces.
The notation T (SEQ y1, …, yn) shows
the translation of a sequence of the OWL ob-
jects from a structural specification into an
RDF collection. A few words should be said
about this way of organizing resources. An
anonymous node, which belongs to the rdf:
list class, and two types of predicates act as a
subject to create a collection. The predicates
are as follows:
- rdf: first – the first element of the
collection (head);
- rdf: rest – the link to sub-
collection (tail).
Table 1. Namespace notation
Prefix name Expansion
@prefix rdf:
http://www.w3.org/1999/02/22
-rdf-syntax-ns#
@prefix rdfs:
http://www.w3.org/2000/01/rd
f-schema#
@prefix owl:
http://www.w3.org/2002/07/o
wl#
@prefix xsd:
http://www.w3.org/2001/XML
Schema#
The head of the collection points to its
first element (an RDF triple object). The tail
contains the remaining items, which are also
organized into a collection (a sub-collection
of the main collection). It looks the same way
– a node (subject) and two predicates (head
and tail), one of which points to the object,
and the second points to the remaining ele-
ments. The tail that contains the last element
of the collection points to the built-in resource
rdf: nil.
_: x will denote an anonymous RDF
triplet node.
So, let's describe the mappings of the
description logic ALC to RDF using OWL 2.
Table 2 shows the mapping rules for all com-
ponents of the ALC syntax.
Моделі та засоби систем баз даних і знань
47
Table 2. DL ALC to RDF mapping rules
ALC OWL 2 RDF
⏉ owl:Thing -
⏊ owl:Nothing -
C, D
Declaration (Class
(C)),
Declaration (Class
(D))
T(C) rdf:type
owl:Class,
T(D) rdf:type
owl:Class
R
Declaration (Ob-
jectProperty(R))
Declaration
(DatatypeProper-
ty(R))
T(R) rdf:type
owl:ObjectPrope
rty,
T(R) rdf:type
owl:DatatypePro
perty
¬C
ObjectComple-
mentOf(C)
_:x rdf:type
owl:Class
_:x
owl:complement
Of T(C)
C⊓D
ObjectIntersection-
Of(C, D)
_:x rdf:type
owl:Class
_:x
owl:intersection
Of T(SEQ C, D)
C⊔D
ObjectUnionOf(C,
D)
_:x rdf:type
owl:Class
_:x owl:unionOf
T(SEQ C, D)
∃R.C
ObjectSomeVal-
uesFrom(R C)
_:x rdf:type
owl:Restriction
_:x
owl:onProperty
T(R)
_x:
owl:someValues
From T(C)
∀R.C
Ob-
jectAllValuesFrom(R
C)
_:x rdf:type
owl:Restriction
_:x
owl:onProperty
T(R)
_x:
owl:allValuesFro
m T(C)
The concepts ⏉ and ⏊ are represented
in OWL by the special classes – owl:Thing
and owl:Nothing. When constructing RDF
triplets, these classes are used in the same
way as within OWL itself.
The images of RDF triplets and their
serialization to N3 notation are shown below.
Definition of concepts C and D
Fig. 3. RDF triplets of C and D definition
image
@prefix : <http://example.com/Ch.owl#>
:C rdf:type owl:Class.
:D rdf:type owl:Class.
Definition of the role R
Fig. 4. RDF triplets of the object property R
definition image
Fig. 5. RDF triplets of the datatype property
R definition image
Since the role R can describe both an
object property and a datatype property, two
RDF triplets for this element were defined.
N3 serialization format for two triples is also
present.
@prefix : <http://example.com/Ch.owl#>
Моделі та засоби систем баз даних і знань
48
:R rdf:type owl:ObjectProperty.
@prefix : <http://example.com/Ch.owl#>
:R rdf:type owl:DatatypeProperty.
Complement of concept C
Fig. 6. RDF triplets of the complement of
concept C image
@prefix : <http://example.com/Ch.owl#>
_:x rdf:type owl:Class;
owl:complementOf :C.
Concept intersection C ⊓ D
Fig. 7. RDF triplets of the concept
intersection image
@prefix : <http://example.com/Ch.owl#>
_:x rdf:type owl:Class;
_:x owl:intersectionOf: (:C :D).
Concept union C ⊔ D
Fig. 8. RDF triplets of the concept union
image
@prefix : <http://example.com/Ch.owl#>
_:x rdf:type owl:Class;
_:x owl:unionOf: (:C :D).
Existential quantification ∃R.C
Fig. 9. RDF triplets of the existential quanti-
fication image
@prefix : <http://example.com/Ch.owl#>
_:x rdf:type owl:Restriction;
owl:onProperty :R;
owl:someValuesFrom:C.
Моделі та засоби систем баз даних і знань
49
Value restriction ∀R.C
Fig. 10. RDF triplets of the value restriction
image
@prefix : http://example.com/Ch.owl#
_:x rdf:type owl:Restriction;
owl:onProperty :R;
owl:allValuesFrom :C.
In cases of mapping the existential
quantification and value restriction concepts,
where the role R reflects a datatype property,
T (DR) instead of the node :C is used, where
DR is the data range.
Number restrictions, nominals
The following constructors are called
number restrictions. If R is a role, C is a con-
cept, and n ≥ 0 is a natural number, then:
- (≤nR) и (≥nR) – at-least and at-
last number restrictions;
- (≤nR.С) и (≥nR.С) – qualified
number restrictions.
In the OWL there is an
owl:cardinality constraint [19]. It describes
a class of all individuals that have exactly
N semantically distinct values (individuals
or data values) for the property concer-
ned, where N is the value of the cardina-
lity constraint. This construct is in fact re-
dundant as it can always be replaced by a
pair of matching owl:minCardinality and
owl:maxCardinality constraints with the
same value. It is included as a convenient
shorthand for the user. Table 3 shows the
mapping rules for number restrictions and
nominal.
Table 3. Number restrictions and nominal to
RDF mapping rules
Exten-
sions
OWL 2 RDF
1 2 3
=nR
ObjectEx-
actCardinal-
ity(n R)
_:x rdf:type
owl:Restriction.
_:x owl:onProperty
T(R).
_:x owl:cardinality
«n»^^xsd:nonNegati
veInteger.
=nR.C
ObjectEx-
actCardinal-
ity(n R C)
_:x rdf:type
owl:Restriction.
_:x owl:onProperty
T(R).
_:x owl:cardinality
«n»^^xsd:nonNegati
veInteger.
_:x owl:onClass
T(C)
≤nR
Object-
MinCardi-
nality(n R)
_:x rdf:type
owl:Restriction.
_:x owl:onProperty
T(R).
_:x
owl:minCardinality
«n»^^xsd:nonNegati
veInteger.
≤nR.C
Object-
MinCardi-
nality(n R
C)
_:x rdf:type
owl:Restriction.
_:x owl:onProperty
T(R).
_:x
owl:minQualifiedCa
rdinality
«n»^^xsd:nonNegati
veInteger.
_:x owl:onClass
T(C)
≥nR
Object-
MaxCardi-
nality(n R)
_:x rdf:type
owl:Restriction.
_:x owl:onProperty
T(R).
_:x
owl:maxCardinality
«n»^^xsd:nonNegati
veInteger.
Моделі та засоби систем баз даних і знань
50
1 2 3
≥nR.C
Object-
MaxCardi-
nality(n R
C)
_:x rdf:type
owl:Restriction.
_:x owl:onProperty
T(R).
_:x
owl:maxQualifiedCa
rdinality
«n»^^xsd:nonNegati
veInteger.
_:x owl:onClass
T(C)
{a}
Objec-
tOneOf(a)
_:x rdf:type
owl:Class.
_:x owl:oneOf
T(SEQ a).
Number restriction =nR
Fig. 11. RDF triplet of the number restriction
=nR
@prefix : <http://example.com/Ch.owl#>
_:x rdf:type owl:Restriction;
owl:onProperty :R;
owl:cardinality
«n»^^xsd:nonNegativeInteger.
Number restriction =nR.C
Fig. 12. RDF triplet of the number restriction
=nR.C
@prefix : <http://example.com/Ch.owl#>
_:x rdf:type owl:Restriction;
owl:onProperty :R;
owl:cardinality
«n»^^xsd:nonNegativeInteger.
owl:onClass :C.
At-least number restriction ≤nR
Fig. 13. RDF triplet of the at-least number
restriction
@prefix : <http://example.com/Ch.owl#>
_:x rdf:type owl:Restriction;
owl:onProperty :R;
owl:minCardinality
«n»^^xsd:nonNegativeInteger.
Qualified number restriction ≤nR.C
Fig. 14. RDF triplet of the qualified number
restriction <nR.C
@prefix : <http://example.com/Ch.owl#>
_:x rdf:type owl:Restriction;
owl:onProperty :R;
Моделі та засоби систем баз даних і знань
51
owl:minQualifiedCardinality
«n»^^xsd:nonNegativeInteger.
owl:onClass :C.
At-last number restriction ≥nR
Fig. 15. RDF triplet of the at-last number
restriction
@prefix : <http://example.com/Ch.owl#>
_:x rdf:type owl:Restriction;
owl:onProperty :R;
owl:maxCardinality «n»
xsd:nonNegativeInteger.
Qualified number restriction ≥nR.C
Fig. 16. RDF triplet of the qualified number
restriction >nR.C
@prefix : <http://example.com/Ch.owl#>
_:x rdf:type owl:Restriction;
owl:onProperty :R;
owl:maxQualifiedCardinality «n»
xsd:nonNegativeInteger.
owl:onClass :C.
Nominal {a}
Fig. 17. RDF triplet of the nominal
@prefix : <http://example.com/Ch.owl#>
_:x rdf:type owl:Class;
owl:oneOf(:a).
Role constructors
If R and S are roles, and C is a con-
cept, then the following expressions are also
roles: R
-
(inverse role), ¬R (complement),
R ⊓ S (intersection), R ⊔ S (union), R ° S
(composition), R
+
(transitive closure), R*
(reflexive-transitive closure), id (C) (role
identity).
In OWL 2 through all the role con-
structors only inverse role is present. This
means that the mapping rules exist only for
this operation. It looks like this in the Table 4.
Table 4. Inverse role to RDF mapping rule
Construc-
tors
OWL 2 RDF
R
-
InverseOb-
jectProperties (R
-
R)
T(R
-
)
owl:invers
eOf T(R)
Fig. 18. RDF triplet for inverse role
Моделі та засоби систем баз даних і знань
52
@prefix : <http://example.com/Ch.owl#>
:R- owl:inverseOf :R
The issue of mapping the remaining
role operators to RDF remains open.
DL axiomatics
The DL axioms include the following
rules:
- concept nesting C ⊑ D;
- concept equivalence C ≡ D;
- role nesting R ⊑ S;
- role equivalence R ≡ S;
- concept individual equivalence
a = b.
Mapping rules are represented in
table 5.
Table 5. DL axiomatics to RDF mapping rules
Axiom OWL 2 RDF
C ≡ D
Equivalent-
Classes (C D)
T(R)
owl:equivalentClass
T(D)
C ⊑ D SubClassOf(C D)
T(R)
rdfs:subClassOf
T(D)
R ⊑ S
SubProjectProp-
ertyOf(R S)
SubDataProper-
tyOf(R S)
T(R)
rdfs:subPropertyOf
T(S)
T(R)
rdfs:subPropertyOf
T(S)
R ≡ S
Equivalen-
tObjectProper-
ties(R S)
Equivalent-
DataProperties(R
S)
T(R)
owl:equivalentPrope
rty T(S)
T(R)
owl:equivalentPrope
rty T(S)
a = b
SameIndividual
(a b)
T(a) owl:sameAs
T(b)
Concept equivalence
Fig. 19. RDF triplet for concept equivalence
@prefix : <http://example.com/Ch.owl#>
:C owl:equivalentClass :D.
Concept nesting
Fig. 20. RDF triplet for concept nesting
@prefix : <http://example.com/Ch.owl#>
:C rdfs:subClassOf :D.
Role equivalence
Fig. 21. RDF triplet for role equivalence
@prefix : <http://example.com/Ch.owl#>
:R owl:equivalentProperty :S
Role nesting
Fig. 22. RDF triplet for role nesting
@prefix : <http://example.com/Ch.owl#>
:R rdfs:subPropertyOf :S
Concept individual equivalence
Fig. 23. RDF triplet for concept individual
equivalence
@prefix : <http://example.com/Ch.owl#>
:a owl:sameAs :b
Conclusion
A method for checking mappings of
description logic to the binary relational data
model using transformations to RDF is de-
scribed in the article. The description of the
approach is given. Bottlenecks and potential
Моделі та засоби систем баз даних і знань
53
problems are identified. Mappings for the DL
axiomatics, as well as for all those construc-
tors of concepts and roles that are implement-
ed in the OWL 2, based on the W3C OWL 2-
to-RDF mapping rules are provided in the
publication. The issue of mapping several of
role constructors to RDF remains open. Map-
ping a binary relational data model to RDF is
in the field for further research.
References
1. Andon P., Reznichenko V., Chystiakova I.
Mapping of Description Logic to the Rela-
tional Data Model. Cybernetics and Systems
Analysis. 2017. 53 (6). P. 963–978.
2. Reznichenko V., Chystiakova I. Binary Rela-
tional Data Model. Problems in Program-
ming. 2017. Vol. 2 (4). P. 96–105.
3. Chystiakova I. Integration of the description
logics axiomatic into relational data model.
Problems in Programming. 2017. Vol. 1(3).
P. 51–58.
4. Chystiakova I. Integration of the description
logics with extensions into relational data
model. Problems in Programming. 2016.
N 4. P. 58–65.
5. Reznichenko V., Chystiakova I. Integration of
the family of extended description logics with
relational data model. Problems in Program-
ming. 2016. N 2–3. P. 38–47.
6. Reznichenko V., Chystiakova I. Mapping of
the Description Logics ALC into the Binary
Relational Data Structure. Problems in Pro-
gramming. 2015. N 4. P. 13–30.
7. Chystiakova I. Ontology-oriented data inte-
gration on the Semantic Web. Problems in
Programming. 2014. N 2–3. P. 188–196.
8. Hazber M.A.G., LI R., GU X., XU G. Integra-
tion Mapping Rules: Transforming Relational
Database to Semantic Web Ontology. Applied
Mathematics & Information Sciences. 2016.
Vol. 3(10). P. 881–901.
9. Hazber M., LI B., XU G., Mosleh M., GU X.,
LI Y. An Approach for Generation of
SPARQL Query from SQL Algebra based
Transformation Rules of RDB to Ontology.
Journal of Software. San Bernardino. 2018.
CA. USA. 2018. Vol. 13(11). P. 573–599.
10. Cerans K., Bumans G. RDB2OWL: a RDB-
to-RDF/OWL Mapping specification Lan-
guage. Proceedings of the 2011 conference on
Databases and Information Systems VI: Se-
lected Papers from the Ninth International
Baltic Conference, DB&IS 2010. Riga, Lat-
via, 5–7 july 2010. P. 139–152.
11. Cerans K., Bumans G. RDB2OWL: A lan-
guage and tool for database to ontology map-
ping. Proceedings of the 27th International
Conference on Advanced Information Sys-
tems Engineering (CAiSE 2015). Stokholm,
Sweeden, 8–12 june 2015. Vol. 1367.
P. 81–88.
12. OWL 2 Web Ontology Language. Mapping to
RDF Graphs (Second Edition). [Online] De-
cember 2012. Available from:
https://www.w3.org/TR/owl2-mapping-to-
rdf/#Translation_of_Axioms_without_Annota
tions. [Accessed: 20 february 2020].
13. R2RML: RDB to RDF Mapping Language.
[Online] September 2012. Available from:
https://www.w3.org/TR/r2rml/. [Accessed: 20
february 2020].
14. Berners-Lee T. Linked data, in design issues
of the WWW. [Online] 2006. Available from:
https://www.w3.org/DesignIssues/LinkedData
.html. [Accessed: 20 february 2020].
15. Michel F., Montagnat J., Zucker C.F. A survey
of RDB to RDF translation approaches and
tools. [Research Report] I3S. 2014. [Online].
2014. Available from: https://hal.archives-
ouvertes.fr/hal-
00903568/file/Rapport_Rech_I3S_v2_-
_Michel_et_al_2013_-
_A_survey_of_RDB_to_RDF_translation_ap
proaches_and_tools.pdf. [Accessed 20 febru-
ary 2020].
16. Description logics with axiomatics. [Online]
2017-2018. Available from:
http://lpcs.math.msu.su/~zolin/dl/pdf/DL_07_
SHIQ.pdf
17. Kontchakov R., Zakharyschev M. An intro-
duction to description logics and query rewrit-
ing. Reasoning Web International Summer
School. Birmingham, UK. 8 september 2014.
Vol. 8714. P. 195–244.
18. Baader F. et al. The Description Logic Hand-
book. 2003. P. 51–55.
19. OWL Web Ontology Language Reference
[Online] 2004. Available from:
https://www.w3.org/TR/owl-ref/
Література
1. Andon P., Reznichenko V., Chystiakova I.
Mapping of Description Logic to the Rela-
tional Data Model. Cybernetics and Systems
Analysis. 2017. 53 (6). P. 963–978.
2. Reznichenko V., Chystiakova I. Binary Rela-
tional Data Model. Problems in Program-
ming. 2017. Vol. 2 (4). P. 96–105.
Моделі та засоби систем баз даних і знань
54
3. Chystiakova I. Integration of the description
logics axiomatic into relational data model.
Problems in Programming. 2017. Vol. 1(3).
P. 51–58.
4. Chystiakova I. Integration of the description
logics with extensions into relational data
model. Problems in Programming. 2016. №
4. P. 58–65.
5. Reznichenko V., Chystiakova I. Integration of
the family of extended description logics with
relational data model. Problems in Program-
ming. 2016. № 2–3. P. 38–47.
6. Reznichenko V., Chystiakova I. Mapping of
the Description Logics ALC into the Binary
Relational Data Structure. Problems in Pro-
gramming. 2015. № 4. P. 13–30.
7. Chystiakova I. Ontology-oriented data inte-
gration on the Semantic Web. Problems in
Programming. 2014. № 2–3. P. 188–196.
8. Hazber M.A.G., LI R., GU X., XU G. Integra-
tion Mapping Rules: Transforming Relational
Database to Semantic Web Ontology. Applied
Mathematics & Information Sciences. 2016.
Vol. 3(10). P. 881–901.
9. Hazber M., LI B., XU G., Mosleh M., GU X.,
LI Y. An Approach for Generation of
SPARQL Query from SQL Algebra based
Transformation Rules of RDB to Ontology.
Journal of Software. San Bernardino. 2018.
CA. USA. 2018. Vol. 13(11). P. 573–599.
10. Cerans K., Bumans G. RDB2OWL: a RDB-
to-RDF/OWL Mapping specification Lan-
guage. Proceedings of the 2011 conference on
Databases and Information Systems VI: Se-
lected Papers from the Ninth International
Baltic Conference, DB&IS 2010. Riga, Lat-
via, 5-7 july 2010. P. 139–152.
11. Cerans K., Bumans G. RDB2OWL: A lan-
guage and tool for database to ontology map-
ping. Proceedings of the 27th International
Conference on Advanced Information Sys-
tems Engineering (CAiSE 2015). Stokholm,
Sweeden, 8-12 june 2015. Vol. 1367.
P. 81–88.
12. OWL 2 Web Ontology Language. Mapping to
RDF Graphs (Second Edition). [Online] De-
cember 2012. Available from:
https://www.w3.org/TR/owl2-mapping-to-
rdf/#Translation_of_Axioms_without_Annota
tions. [Accessed: 20 february 2020].
13. R2RML: RDB to RDF Mapping Language.
[Online] September 2012. Available from:
https://www.w3.org/TR/r2rml/. [Accessed: 20
february 2020].
14. Berners-Lee T. Linked data, in design issues
of the WWW. [Online] 2006. Available from:
https://www.w3.org/DesignIssues/LinkedData
.html. [Accessed: 20 february 2020].
15. Michel F., Montagnat J., Zucker C.F.. A sur-
vey of RDB to RDF translation approaches
and tools. [Research Report] I3S. 2014.
[Online]. 2014. Available from:
https://hal.archives-ouvertes.fr/hal-
00903568/file/Rapport_Rech_I3S_v2_-
_Michel_et_al_2013_-
_A_survey_of_RDB_to_RDF_translation_ap
proaches_and_tools.pdf. [Accessed 20 febru-
ary 2020].
16. Description logics with axiomatics. [Online]
2017-2018. Available from:
http://lpcs.math.msu.su/~zolin/dl/pdf/DL_07_
SHIQ.pdf
17. Kontchakov R., Zakharyschev M. An intro-
duction to description logics and query rewrit-
ing. Reasoning Web International Summer
School. Birmingham, UK. 8 september 2014.
Vol. 8714. P. 195–244.
18. Baader F. et al. The Description Logic Hand-
book. 2003. P. 51–55.
19. OWL Web Ontology Language Reference
[Online] 2004. Available from:
https://www.w3.org/TR/owl-ref/
Received 18.10.2020
About the author:
Inna Chystiakova,
junior researcher at the Institute of
software systems of NASU.
The number of publications in
Ukrainian journals – 10.
The number of publications in
foreign journals – 1.
Hirsh index is 5.
https://orcid.org/0000-0001-7946-3611.
Affiliation:
Institute of software systems of NASU
03187, Kyiv,
pr. Glushkova, 40, build 5.
Tel.: +38(066)8477784.
E-mail: inna_islyamova@ukr.net.
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