Databases Reference
In-Depth Information
The moral of this example is that to allow FO-rewritability, TBoxes should not
contain axioms with disjunctive information (which can be satisfied in essentially
different ways when applied to ABoxes). The TBox in Example 4 is formulated
in the DL
.
The data complexity of answering CQs over ontologies formulated in various
DLs has been intensively investigated since 2005; see, e.g., [12,39,11,49,4]. Thus,
answering CQs over
ALC
EL
ontologies is
P
-complete for data complexity, while for
ALC
-hard. One of the results of this research was the inclusion in the
current W3C standard Web Ontology Language
it is
coNP
of a special sublanguage
(or profile) that is suitable for OBDA with databases and called
OWL 2
OWL 2 QL
.The
DLs underlying
OWL 2 QL
belong to the so-called
DL-Lite
family [11,4]. Below,
we present
OWL 2 QL
in the DL parlance rather than the
OWL 2
syntax.
contains
individual names a
i
,
concept names A
i
,
and
role names P
i
(
i
=1
,
2
,...
).
Roles R
,
basic concepts B
and
concepts C
are
defined by the grammar:
The language of
OWL 2 QL
P
i
,
R
::=
P
i
|
B
::=
⊥|
A
i
| ∃
R,
C
::=
B
| ∃
R.B
(here
P
i
is the inverse of
P
i
and
∃
R
is regarded as an abbreviation for
∃
R.
).
An
OWL 2 QL
TBox
,
T
, is a finite set of
concept
and
role inclusions
of the form
B
C,
R
1
R
2
and
concept
and
role disjointness constraints
of the form
B
1
B
2
⊥
,
1
R
2
⊥
.
Apart from this,
T
may contain assertions stating that certain roles
P
i
are
reflexive and irreflexive. Note that symmetry and asymmetry of a role
R
can be
expressed in
OWL 2 QL
as, respectively,
R
−
R
−
⊥
R
and
R
.
An
, is a finite set of
assertions
of the form
A
k
(
a
i
)and
P
k
(
a
i
,a
j
)and
inequality constraints a
i
OWL 2 QL
ABox
,
A
=
a
j
for
i
=
j
.
T
and
A
together consti-
tute the
knowledge base
(KB)
).
It is to be noted that concepts of the form
K
=(
T
,
A
∃
R.B
can only occur in the right-
OWL 2 QL
.Aninclusion
B
∃
R.B
can be
hand side of concept inclusions in
regarded as an abbreviation for three inclusions:
B
∃
R
B
R
B
,
∃
B
and
R
B
R,
where
R
B
is a fresh role name. Thus, inclusions of the form
B
∃
R.B
are
just convenient syntactic sugar. To simplify presentation, in the remainder of
this chapter we consider the sugar-free
OWL 2 QL
, assuming that every concept
inclusion is of the form
B
1
B
2
,whereboth
B
1
and
B
2
are basic concepts.
