Databases Reference
In-Depth Information
Example 8.
Consider an ontology
T
with the axioms
RA
∃
worksOn.Project,
(3)
Project
∃
isManagedBy.Prof,
(4)
worksOn
−
involves,
(5)
isManagedBy
involves
(6)
and the CQ asking to find those who work with professors:
y,z
worksOn
(
x, y
)
Prof
(
z
)
,
q
(
x
)=
∃
∧
involves
(
y,z
)
∧
or graphically:
y
q
(
x
)
x
z
worksOn
involves
Prof
Observe that if the canonical model
C
K
of
K
=(
T
,
A
), for some ABox
A
, contains
RA
C
K
and
b
Project
C
K
,then
individuals
a
∈
∈
C
K
must also contain the following
fragments:
a
u
v
b
w
isManagedBy
involves
isManagedBy
involves
worksOn
involves
−
RA
Project
Prof
Project
Prof
Here the vertices
are either named individuals from the ABox or anonymous
witnesses for the existential quantifiers (generated by the axioms (3) and (4)).
It follows then that
a
is an answer to
◦
RA
C
K
becausewehavethe
q
(
x
)if
a
∈
following homomorphism from
q
to
C
K
:
y
q
(
x
)
x
z
worksOn
involves
Prof
u
worksOn
involves
−
involves
a
RA
Prof
v
isManagedBy
Project
Alternatively, if
a
is in both
RA
C
K
and
Prof
C
K
, then we obtain the following
homomorphism:
Prof
z
y
q
(
x
)
x
worksOn
u
v
worksOn
involves
−
involves
a
RA
Prof
isManagedBy
Project
Another option is to map
x
and
y
to ABox individuals,
a
and
b
,andif
b
is in
Project
C
K
, then the last two atoms of
q
can be mapped to the anonymous part:
y
q
(
x
)
x
z
worksOn
involves
Prof
involves
Project
Prof
w
isManagedBy
