Database Reference
In-Depth Information
R
s
:
FLIGHT
(
·,·,·,·
),
GEO
(
·,·,·
)
ROUTES
(
·,·,·
),
INFO FLIGHT
(
·,·,·,·
),
SERVES
(
·,·,·,·
)
R
t
:
(Σ
st
)
FLIGHT(src,dest,airl,dep)
−→
∃
f#
∃
arr
ROUTES(f#,src,dest)
∧
INFO FLIGHT(f#,dep,arr,airl)
(Σ
st
)
FLIGHT(city,dest,airl,dep)
∧
GEO(city,country,popul)
−→ ∃
phone SERVES(airl,city,country,phone)
(Σ
st
)
FLIGHT(src,city,airl,dep)
∧
GEO(city,country,popul)
−→ ∃
phone SERVES(airl,city,country,phone)
∀
f#
∀
s
∀
d
∀
s
∀
d
ROUTES
(
f#
,
s
,
d
)
∧
ROUTES
(
f#
,
s
,
d
)
→
s
=
s
∧
d
=
d
(Σ
t
)
(Σ
t
)
∀
f#
∀
s
∀
d
ROUTES
(
f#
,
s
,
d
)
→
∃
a
∃
a
∃
d
INFO FLIGHT
(
f#
,
d
,
a
,
a
)
Figure 3.1 A complete schema mapping
M
=(R
s
,
R
t
,
Σ
st
,
Σ
t
)
In addition, one might impose constraints on target instances, for example, keys and
foreign keys, or other database integrity constraints. Let
Σ
t
be a set of such constraints,
expressed by logical sentences over R
t
.
A schema mapping is then defined as a quadruple
M
=(R
s
,
R
t
,
Σ
st
,
Σ
t
)
,
or just
Σ
st
), when there are no target constraints.
An example of a schema mapping was shown in
Figure 1.3
on page
7
. That schema had
no target constraints. If one expands it with the rules stating that
f#
is a key for
ROUTES
and
f#
occurring in
INFO FLIGHT
is a foreign key referencing
ROUTES
, one would arrive
at the complete schema mapping shown in
Figure 3.1
.
M
=(R
s
,
R
t
,
3.2 Solutions
Now assume that
S
is a
source instance
, i.e., a database instance over R
s
.Thenatarget
instance
T
is called a solution for
S
under
M
if and only if
S
and
T
together satisfy all
the stds in
Σ
st
,and
T
satisfies all the constraints in
Σ
t
.Thatis,
T
is a solution for
S
under
M
if
(
S
,
T
)
|
=
Σ
st
and
T
|
=
Σ
t
.
For mappings without target constraints, we only require (
S
,
T
)
|
=
Σ
st
.
