Data Exchange between Relational Knowledge Bases
in the Web of Data
Tadeusz Pankowski
Institute of Control and Information Engineering, Pozna´n University of Technology, Pozna´n, Poland
Keywords:
DL Knowledge Bases, Data Integration, Integrity Constraints, Data Exchange, Databases vs. Knowledge
Bases.
Abstract:
An important component of the Web of Data is formed by data originally stored in relational databases. The
relational data along with its schemes and integrity constraints is translated into a knowledge base, that we
call a relational knowledge base (RKB), residing on the Web. It is important to preserve semantics in data-to-
knowledge transformation, as well as in knowledge-to-knowledge exchange between two RKBs. We discuss
these issues and propose an algorithm for checking whether a mapping between two RKBs is semantics pre-
serving. The algorithm is based on the chase procedure.
1 INTRODUCTION
Technologies of the Semantic Web enables web-wide
integration of data coming from various sources. In
this way the Web of Data is created and can be also
perceived as a giant knowledge base. The extensional
layer of this knowledge base consists of an RDF graph
(or a corresponding OWL specification), and the in-
tensional layer is a set of axioms (in RDFS or OWL).
Very often the data presented in the Web comes from
relational databases. Thus, the similarities and differ-
ences between databases and knowledge bases, and
combining these technologies in data integration ac-
tivities, has been an important and attractive field of
research since many years (Abiteboul et al., 1995; Re-
iter, 1982; Motik et al., 2009). Now, as a formal foun-
dation of knowledge bases serve Description Logics
(DLs) (Baader et al., 2003), and DL knowledge base
(or DL ontology) is a pair K = (T , A), where T is
a set of axioms modeling the intensional knowledge
(the TBox axioms), and A is a set of assertions form-
ing the extensional knowledge (the ABox assertions).
Some recent results of representing relational
databases in the Semantic Web are surveyed in (Se-
queda et al., 2011) and some solutions were proposed
in (Sequeda et al., 2012; Arenas et al., 2012; Poggi
et al., 2008; Pankowski, 2012b; Pankowski, 2013a).
A relationship between relational databases and DL
knowledge bases has been studied in (Motik et al.,
2009; Pankowski, 2012a).
There are three main differences between
databases and knowledge bases making the transla-
tion between them difficult: (a) databases are based
on CWA (Closed World Assumption) while knowl-
edge bases on OWA (Open World Assumption); (b)
databases accept UNA (Unique Name Assumption)
while knowledge bases usually do not accept it;
(c) integrity constraints in databases are interpreted
as checks while in knowledge bases all rules are
deductive rules. It turns out that incorporating
integrity constraints into knowledge bases is the most
challenging issue.
In this paper, we follow the concept of an ex-
tended DL knowledge base (EKB), where the set T
of TBox axioms is divided into standard TBox ax-
ioms, S , and integrity constraint TBox axioms, C
(Motik et al., 2009). We will use the notion of
EKB to represent a relational database in DL. We
define a data-to-knowledge exchange (dk-exchange)
system that defines translation of relational database
schema, its integrity constraints and instances into
an EKD referred to as a relational knowledge base
(RKB). The semantics of data should not be lost by
the translation, i.e. consistent (inconsistent) databases
are transformed into consistent (inconsistent) knowl-
edge bases. We propose and discuss an algorithm for
checking whether a mapping between two RKBs is
semantics preserving.
In Section 2 we introduce a running example, and
in Section 3 we review some basic notions of rela-
tional databases. Translation of databases into RKBs
is discussed in Section 4. In Section 5 an algorithm
304
Pankowski T..
Data Exchange between Relational Knowledge Bases in the Web of Data.
DOI: 10.5220/0004555903040309
In Proceedings of the 15th International Conference on Enterprise Information Systems (ICEIS-2013), pages 304-309
ISBN: 978-989-8565-59-4
Copyright
c
 2013 SCITEPRESS (Science and Technology Publications, Lda.)

for reasoning about data exchange between RKBs is
proposed. Section 6 concludes the paper.
2 MOTIVATING SCENARIO
As the running example we will consider ER dia-
grams in Figure 1 describing students, courses and
exams taken by students, in databases corresponding
to two universities, named a and b, respectively. In a
(Figure 1(a)) a student is a specialization of a person.
Farther on, all names will be prefixed by the corre-
sponding database name (e.g. a:Student, b:SId).
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Ă͗ŽƵƌƐĞ
ϭ
E
Ă͗džĂŵ
E
ϭ
ď͗^ƚƵĚĞŶƚ
ď͗ŽƵƌƐĞ
ϭ
ϭ
;ĂͿ
;ďͿ
ϭ
E
ď͗džĂŵ
E
ϭ
Figure 1: Two ER diagrams of two university domains.
Besides syntactic differences between a and b,
there is also an important semantic difference be-
tween them: in a, Faculty is an attribute of Student,
while in b – an attribute of Exam meaning that a stu-
dent can be enrolled in many faculties. The corre-
sponding relation schemes are listed in Figure 2.
a:Person(a:PId,a:Name)
a:Student(a:SId,a:Faculty)
a:Course(a:CId)
a:Exam(a:EId,a:ESId,a:Course,a:Grade)
b:Student(b:SId,b:Name)
b:Course(b:CId)
b:Exam(b:EId,b:ESId,b:Course,b:Faculty,b:Grade)
Figure 2: Relation schemes corresponding to ERDs.
There must be also some integrity constraints de-
fined for these relation schemes, such as: a:SId is the
primary key for a:Student, a:SId is also a foreign key
referring to a:PId in a:Person, a:Faculty must be not
NULL, b:Name can be NULL, etc.
In our scenario, we are interested in:
1. Creation of DL knowledge bases K
a
and K
b
rep-
resenting databases DB
a
and DB
b
, i.e. creation of
a dk-exchange system, that should be semantics
preserving.
2. Reasoning about mappings between K
a
and K
b
,
and – in consequences – between DB
a
and DB
b
.
The question is whether there exists a mapping
and the corresponding data transformation that
preserves information and semantics. Intuitively,
we see that such a mapping can be defined from
DB
a
to DB
b
but not inversely (because of differ-
ences in semantics of Faculty in both databases).
3 RELATIONAL DATABASES
A (relational) database schema (db-schema) is a pair
(R, IC), where R = {R
1
, . . . , R
n
} is a relation schema
consisting of a set of relation symbols, and IC is a
set of integrity constraints over R. Each relation sym-
bol R ∈ R has a type, which is a nonempty finite set
att(R) of attributes. Without loss of generality, we
can assume that types of relation symbols are pair-
wise disjoint.
Let Const be a countable infinite set of constants,
and NULL be a reserved symbol not in Const. An in-
stance I of R is a finite set of facts (or atoms) of the
form R(A
1
: c
1
, . . . , A
m
: c
m
), where R ∈ R, att(R) =
{A
1
, . . . , A
m
}, and c
i
∈ Const∪ {NULL}, 1 ≤ i ≤ m.
Integrity constraints in databases play a dual role.
They can be used in data reasoning tasks, such as
checking the correctness of database data, as well as
in schema reasoning tasks, such as computing query
containment.
We assume that IC = Unique∪ NotNull ∪ PKey∪
FKey∪ Inherit, where:
1. Unique is a set of unique integrity constraints, i.e.
expressions of the form unique(R, A), where R ∈
R, A ∈ att(R). An instance I of R is consistent with
unique(R, A
k
), if for every i, 0 ≤ i ≤ m, I satisfies
the formula
R(t
1
) ∧ R(t
2
) ∧t
1
.A
k
= t
2
.A
k
∧
t
1
.A
k
6= NULL ∧ t
2
.A
k
6= NULL∧
t
1
.A
i
6= NULL ∧t
2
.A
i
6= NULL ⇒ t
1
.A
i
= t
2
.A
i
.
2. NotNull is a set of not-null integrity constraints,
i.e. expressions of the form notnull(R, A
k
). An
instance I of R is consistent with notnull(R, A
k
),
if for any fact R(t) ∈ I, t.A
k
is a constant, i.e. if I
satisfies the formula
R(t) ⇒ t.A
k
6= NULL.
3. PKey is a set of primary key integrity constraints,
i.e. expressions of the form pkey(R, A
k
). An in-
stance I of R is consistent with pkey(R, A
k
) if it is
consistent with unique(R, A
k
), and notnull(R, A
k
).
4. FKey is a set of foreign key integrity constraints.
Let R, R
′
∈ R, A ∈ att(R), and A
′
∈ att(R
′
). A
DataExchangebetweenRelationalKnowledgeBasesintheWebofData
305

foreign key integrity constraint is an expression
of the form fkey(R, A, R
′
, A
′
). An instance I of R
is consistent with fkey(R, A, R
′
, A
′
) if I satisfies
unique(R
′
, A
′
), and
R(t) ∧t.A 6= NULL ⇒ ∃t
′
.(R
′
(t
′
) ∧ t
′
.A
′
= t.A)
5. Inherit is a set of inheritance integrity con-
straints, i.e. pairs of the form (pkey(R, A),
fkey(R, A, R
′
, A
′
)). An instance I of R is consis-
tent with (pkey(R, A), fkey(R, A, R
′
, A
′
)), if I sat-
isfies both pkey(R, A) and f key(R, A, R
′
, A
′
).
Let (R, IC) be a db-schema and I be an instance of
R. A database DB = (R, IC, I) is consistent, if I sat-
isfies (is a model of) all integrity constraints, denoted
I |= IC. Otherwise we say that DB is inconsistent.
For the database DB
a
with relation schema in Fig-
ure 2, we assume (the prefix a : is omitted):
IC
a
= {pkey(Person, PId), pkey(Student, SId), pkey(
Course, CId), pkey(Exam, EId), fkey(Student, SId,
Person, PId), pkey(Exam, ESId, Student, SId),
pkey(Exam, Course, Course, CId), notnull(Student,
Faculty), notnull(Exam, Grade)}.
Analogously, for DB
b
. Note, that Name can be NULL
in both databases.
4 DK-EXCHANGE
4.1 Translation of a Database
While translating a relational database into a DL
knowledge base, the following should be taken into ac-
count:
1. A traditional DL knowledge base understood as a
pair (T , A) is unable to model integrity constraints
(Motik et al., 2009). The reason is two-fold: firstly,
axioms in T are interpreted under the standard
first-order semantics and are treated as deductive
rules and not as checks, and secondly, the UNA is
not accepted in general in DL knowledge bases, it
means that two different individual names can de-
note the same individual.
2. In the translation, semantics of the database should
be preserved, i.e. any consistent (inconsistent)
database should be translated into a consistent (in-
consistent) DL knowledge base.
Now, we define a relational knowledge base
(RKB) that is a DL knowledge base adequately rep-
resenting a relational database. RKB is based on the
concept of EKB (Motik et al., 2009). We propose and
discuss a system of TBox axioms, which properly rep-
resents a relational database defined in the previous
section.
A relational knowledge base is a tuple RKB =
(N, S , C , A), where:
1. N is the vocabulary of RKB, consisting of a set
N
Ind
of individual names, a set N
Cl
of class names
(or atomic concepts), a set N
OP
of object property
names (or atomic roles).
2. S is a finite set of standard TBox axioms, which
are treated as deductive rules and can infer new as-
sertions.
3. C is a finite set of integrity constraint TBox ax-
ioms, which are treated as checks, and must be sat-
isfied by any minimal Herbrand model of the set of
assertions implied by A and S . Axioms in C can-
not imply new assertions.
4. A is a set of ABox assertions, i.e. class member-
ships and properties of individual objects.
The translation is made by a data-to-knowledge ex-
change (dk-exchange) system M = (τ, Σ), such that
for each db-schema (R, IC) and every instance I of R,
M (R, IC, I) = (τ(R, IC), Σ(I)) = (N, S , C , A), where
τ(R, IC) = (N, S, C ), and Σ(I) = A.
Creating Vocabulary. Let ∆
Var
be a countable infi-
nite set of labeled nulls disjoint from the set of con-
stants. Labeled nulls, denoted X, V, X
1
, V
1
, ..., are used
as ”fresh” Skolem terms, which are placeholders for
unknownvalues, and can thus be seen as variables (Fa-
gin et al., 2005). The vocabulary N = N
Ind
∪N
Cl
∪N
OP
,
is created as follows: (1) The set N
Ind
of individual
names consists of the union of Const and ∆
Var
. (2)
There are predefined class names Tuple and Val of,
respectively, individuals called tuples and individuals
called attribute values. (3) For each relation symbol
R ∈ R, there is a class name C
R
∈ N
Cl
, every individ-
ual in C
R
is a tuple. (4) For each attribute A ∈ att(R),
there is a class name C
A
∈ N
Cl
(every individual in
C
A
is an attribute value), and an object property name
P
A
∈ N
OP
; the object property P
A
connects tuples in C
R
with attribute values in C
A
.
Creating StandardTBox Axioms. The set S of standard
TBox axioms is given in Table 1. All these axioms are
deductive rules.
Table 1: Standard TBox axioms of relational knowledge
base.
Constraints of relational db DL
S1 R ∈ R C
R
⊑ Tuple
S2 A ∈ att(R), R ∈ R C
A
⊑ Val
S3 range of P
A
∃P
−
A
⊑ C
A
S4 domain of P
A
∃P
A
⊑ C
R
S5 unique(R, A) (func P
−
A
)
S6 (pkey(R, A), fkey(R, A, R
′
, A
′
)) P
A
⊑ P
A
′
(S1) and (S2) belong to translation of facts that R ∈ R
and A ∈ att(R); they say that all tuple names in C
R
,
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306

and all attribute value names in C
A
must be inserted
into classes Tuple and Val, respectively. (S3) and
(S4) belong to translation of the fact that A ∈ att(R),
where: (S3) says that any individual belonging to the
range of P
A
must be inserted into C
A
, and any indi-
vidual belonging to the domain of P
A
must be inserted
into C
R
. (S5) is result of translation of a unique con-
straint unique(R, A), and enforces equality between x
1
and x
2
, if all P
A
(x
1
, v
1
), P
A
(x
2
, v
2
), and v
1
= v
2
hold.
(S6) results of the translation of an inheritance con-
straint (pkey(R, A), fkey(R, A, R
′
, A
′
)), and says that
extension of P
A
must be inserted into the extension of
P
A
′
.
Creating Integrity Constraint TBox Axioms. The set C
of TBox ic-axioms is given in Table 2. Note that ic-
axioms are checks, so we expect that the value of such
an axiom is either TRUE or FALSE.
Table 2: Integrity constraint TBox axioms of relational
knowledge base.
Constraints of relational db DL
C1 disjointness Tuple ⊑ ¬Val
C2 A ∈ att(R), R ∈ R (func P
A
)
C3 notnull(R, A) C
R
⊑ ∃P
A
C4 fkey(R, A, R
′
, A
′
) ∃P
−
A
⊑ ∃P
−
A
′
C5 (pkey(R, A), f key(R, A, R
′
, A
′
)) C
R
⊑ C
R
′
(C1) tests disjointness of Tuple and Val. (C2) be-
longs to translation of A ∈ att(R) and checks if P
A
has the functional property. (C3) is result of trans-
lation of notnull(R, A) and tests if any tuple name in
C
R
is in domain of P
A
. (C4) is result of translation of
fkey(R, A, R
′
, A
′
), and tests the inclusion of the range
of P
A
in the range of P
A
′
. (C5) belongs to the result of
the translation of (pkey(R, A), fkey(R, A, R
′
, A
′
)), and
tests the inclusion of C
R
in C
R
′
.
Creating ABox Assertions. ABox assertions are ex-
pressions of the form: C(a), P(a
1
, a
2
), and a
1
= a
2
,
where C ∈ N
Cl
, P ∈ N
OP
, and a, a
1
, a
2
∈ N
Ind
. Trans-
lation of an instance I of R can be performed using
Algorithm 1.
Algorithm 1: Creating ABox assertions.
Input: Instance I of R, and an empty ABox A.
Output: ABox assertions in A representing I.
for each R(t) ∈ I
U
R,t
:= {A ∈ att(R) | t.A 6= NULL}
X := a fresh labeled null in ∆
Var
if U
R,t
=
/
0 then
A := A ∪ {C
R
(X)}
else
for each A ∈ U
R,t
A := A ∪ {P
A
(X, t.A)}
end
4.2 Semantics Preservation
One of the most challenging issues in dk-exchange
is to show that the semantics of the source data is
not lost by the transformation into a knowledge base.
The preservation of semantics of a dk-exchange sys-
tem M = (τ, Σ) can be understood in two ways:
1. Soundness. M = (τ, Σ) is sound w.r.t. seman-
tics preservation if every consistent database (R, IC, I)
is transformed into a consistent relational knowledge
base (N, S , C , A), i.e.
I |= IC∧τ(R, IC) = (N, S , C )∧Σ(I) = A ⇒ A ∪S |=
mHm
C .
2. Completeness. M = (τ, Σ) is complete w.r.t. se-
mantics preservation if every inconsistent database
(R, IC, I) is transformed into an inconsistent relational
knowledge base (N, S, C , A), i.e.
I 6|= IC∧τ(R, IC) = (N, S , C )∧Σ(I) = A ⇒ A ∪S 6|=
mHm
C .
It can be shown (Pankowski, 2013b) that the dk-
exchange system M = (τ, Σ), is both sound and com-
plete w.r.t. semantics preservation.
5 REASONING ABOUT
KBS-MAPPING
A knowledge base schema mapping (kbs-mapping)
from a source kb-schema R
s
= (N
s
, S
s
, C
s
) to a tar-
get kb-schema R
t
= (N
t
, S
t
, C
t
), is defined by a finite
set Γ
st
of source to target dependencies (STDs) (Fagin
et al., 2005), i.e. implications of the form
∀x, v.(ϕ
s
(x, v) ⇒ ∃x
′
, v
′
.ϕ
t
(x, x
′
v, v
′
)),
where ϕ
s
and ϕ
t
are conjunctions of atomic formulas
over N
s
and N
t
, respectively.
Example 5.1. For the knowledge bases corresponding
to databases in Figure 2, we can define the following
kbs-mappings:
Γ
ab
= {
a : p(x, v) ⇒ b : p(x, v),
for p ∈ {SId, CId, EId, ESId, Course, Grade},
a : Name(x, v) ∧ a : Student(x) ⇒ b : Name(x, v),
a : SId(x, v
1
) ∧ a : Faculty(x, v
2
) ∧ a : EId(y, v
3
)∧
a : ESId(y, v
1
) ⇒ b : Faculty(y, v
2
)}
Γ
ba
= {
b : p(x, v) ⇒ a : p(x, v), for p ∈ { SId,
Name, CId, EId, ESId, Course, Grade},
b : ESId(x, v
1
) ∧ b : Faculty(x, v
2
) ⇒
∃y.(a : SId(y, v
1
) ∧ a : Faculty(y, v
2
))}
The crucial problem is if any consistent source
knowledge base is transformed by the given set Γ of
DataExchangebetweenRelationalKnowledgeBasesintheWebofData
307

STDs, into a consistent target knowledge base. It can
be easily seen for our running example that R
a
and R
b
are not semantically equivalent – integrity constraints
for R
a
are more restrictive than those of R
b
. Thus, we
can expect that:
• any consistent knowledge base with schema R
a
is
transformed via Γ
ab
into a consistent knowledge
base with schema R
b
;
• there is a consistent knowledge base with schema
R
b
that is transformed via Γ
ba
into an inconsistent
knowledge base with schema R
a
.
In order to perform such reasoning, we use the
chase procedure (Maier et al., 1979; Fagin et al.,
2005). Input, output and steps of this procedure are
as follows:
1. Input. A source kb-schema R
s
= (N
s
, S
s
, C
s
) repre-
senting a db-schema (R
s
, IC
s
), a target kb-schema
R
t
= (N
t
, S
t
, C
t
), and a set Γ
st
of STDs from R
s
to
R
t
.
2. Output. The decision whether Γ
st
maps any con-
sistent knowledge base with the kb-schema R
s
into
a consistent knowledge base with the schema R
t
.
3. Steps. (1) Construct a tableau A
s
of assertions
such that (N
s
, S
s
, C
s
, A
s
) forms a consistent knowl-
edge base. Moreover, A
s
should be a ”well suited”
source instance for the next steps in the chase pro-
cedure. (2) Proceed the chase from A
s
to A
t
using
Γ
st
and axioms from S
t
. (3) Verify consistency of
(N
t
, S
t
, C
t
, A
t
).
Algorithm 2: Constructing the tableau A
s
.
A
0
:=
/
0;
for each γ ∈ Γ
st
.
let ϕ
s
(x, v) be the left-hand side of γ;
if ϕ
s
(x, v) consists of one atom P
A
(x, v) then
Modify A
0
in such a way that the formula
∃x
1
, x
2
, v.P
A
(x
1
, v) ∧ P
A
(x
2
, v)
is satisfied in A
0
.
if ϕ
s
(x, v) consists of one atom C
R
(x) then
Modify A
0
in such a way that the formula
∃x.C
R
(x)
is satisfied in A
0
.
else // there are more atoms than one in ϕ
s
(x, v)
Let v = (v
1
, ..., v
n
) and v
′
= (v
′
1
, ..., v
′
n
) be disjoint
sets of variables. By ω = [v
1
7→ w
1
, ..., v
n
7→ w
n
],
where w
i
∈ {v
i
, v
′
i
} we denote a substitution
replacing v
i
either with itself or with v
′
i
. The set
Ω of all such substitutions has 2
n
elements.
Then, from ϕ
s
(x, v) we obtain the following
formula consisting of 2
n
conjunctions
∃x, v, v
′
.(ϕ
s
(x, v)[ω
1
] ∧ · ·· ∧ ϕ
s
(x, v)[ω
2
n
] ∧ v 6= v
′
).
For each ω ∈ Ω determine a substitution ν
ω
of
variables in x with a newly invented variable
names x
ω
, denoted ν
ω
= [x 7→ x
ω
]. Then the
following formula is created
Φ ≡ ∃x
ω
1
, . . . , x
ω
2
n
, v, v
′
.(
ϕ
s
(x
ω
1
, v)[ω
1
] ∧ · ·· ∧ ϕ
s
(x
ω
2
n
, v)[ω
2
n
] ∧ v 6= v
′
).
Modify A
0
so that A
0
satisfies Φ.
end for each R ∈ R, A ∈ att(R)
if notnull(R, A) 6∈ IC then
Modify A
0
in such a way that the formula
∃x.C
R
(x) ∧ ¬∃v.P
A
(x, v)
is satisfied in A
0
.
end
Closing. Chase with respect to S
s
∪ C
s
, i.e.
A
0
S
s
∪C
s
−→ A
s
Transformation. Chase with respect to Γ
st
, i.e.
A
s
Γ
st
−→ A
1
Repairing. Chase with respect to S
t
, i.e.
A
1
S
t
−→ A
t
Verifying. It must be checked if axioms in C
t
are satis-
fied in A
t
, i.e. if the following entailment holds:
A
t
|=
mHm
C
t
.
Example 5.2. For Γ
ba
in Example 5.1, we have the
following formulas mentioned in Algorithm 2:
∃x
1
, x
2
, v.b : p(x
1
, v) ∧ b : p(x
2
, v),
for p ∈ {SId, Name, CId, EId, ESId, Course, Grade},
∃x
1
, x
2
, x
3
, x
4
, v
1
, v
2
, v
′
1
, v
′
2
.(
p : ESId(x
1
, v
1
) ∧ b : Faculty(x
1
, v
2
)∧
p : ESId(x
2
, v
1
) ∧ b : Faculty(x
2
, v
′
2
)∧
p : ESId(x
3
, v
′
1
) ∧ b : Faculty(x
3
, v
2
)∧
p : ESId(x
4
, v
′
1
) ∧ b : Faculty(x
4
, v
′
2
)∧
v
1
6= v
′
1
∧ v
2
6= v
′
2
),
∃x.b : Student(x) ∧ ¬∃v.b : Name(x, v).
We start the chase procedure with the first formula
in Example 5.2. Then we have b : SId(X
1
, V
1
) and
b : SId(X
2
, V
1
). Next, using (S4) and (S5), we obtain
b : Student(X
1
) and X
1
= X
2
. The final form of A
b
is
presented in Figure 3 (prefixes b : are omitted), where
additionally: V
6
= V
1
, V
12
= V
3
, V
8
= V
15
= V
16
= V
4
,
and V
6
6= V
12
, V
10
6= V
11
.
A fragment of the tableau A
a
, being the result of
applying Γ
ba
to A
b
, is presented in Figure 4 (again,
ICEIS2013-15thInternationalConferenceonEnterpriseInformationSystems
308

Student SId Name
X
1
V
1
V
2
X
3
V
3
V
2
X
11
V
19
Course CId
X
4
V
4
Exam EId ESId Course Faculty Grade
X
6
V
5
V
6
V
8
V
10
V
9
X
8
V
7
V
6
V
8
V
11
V
9
X
9
V
13
V
12
V
15
V
10
V
17
X
10
V
14
V
12
V
16
V
11
V
18
Figure 3: Tabular representation of A
b
as an input tableau
to Γ
ba
.
Person
PId Name
X
1
V
1
V
2
X
3
V
3
V
2
X
11
V
19
Student SId Faculty
X
1
V
1
V
10
X
1
V
1
V
11
X
3
V
3
V
10
X
3
V
3
V
11
Figure 4: Tabular representation of a fragment of A
a
being
the result of applying Γ
ba
against A
b
from Figure 3.
prefixes a : are omitted). We see that consistency
of A
a
requires that V
10
= V
11
. However, this equal-
ity contradicts the assumption in A
b
(i.e. V
10
6= V
11
).
Thus, the target knowledge base is inconsistent. We
see that Γ
ba
does not preserve semantics, because
a consistent knowledge base with kb-schema R
b
is
transformed into inconsistent knowledge base with
kb-schema R
a
. In this case, the reason is that kb-
schemes R
a
and R
b
are not semantically equivalent.
6 CONCLUSIONS
In this paper we discuss the problem of semantics
preservation in data exchange between two relational
knowledge bases (RKBs) in the Web of Data. RKBs
are important components of Web of Data since they
arise as results of translation relational databases
along with their integrity constraints into knowledge
bases. In this paper we adapt the concept of DL ex-
tended knowledge bases (Motik et al., 2009). Data
exchange between RKBs is a vital problem in data
integration over the Web (Brzykcy et al., 2008). We
sketch an algorithm that checks whether a given map-
ping between two RKBs is semantics preserving, that
is whether it maps a consistent source RKB into a
consistent target RKB.
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