Database Reference
In-Depth Information
In the last TP-XFD a
key
for the context subtree must be given (we assume that the context subtree
is uniquely determined by the
title
of the publication) (see Buneman et al., 2003).
Note that TP-XFDs are XPath expressions, so their semantics is precisely defined. Moreover, they
can be easily incorporated into XQuery-based procedures exploiting these constraints.
Definition 12.
We say that a TP-XFD
F
(
x'
) is defined over a schema
S
(
x
), if
x'
∧
x
and
type
S
(
x
) =
type
F
(
x
) for each
x
∧
x'
.
Definition 13.
(
satisfaction of TP-XFD
) An instance
I
= (
S
(
x
), Ω) satisfies a TP-XFD
F
(
x'
) defined over
S
(
x
), if for any two valuation ω
1
, ω
2
∧
Ω the following implication holds
ω
1
(
x'
) = ω
2
(
x'
)
∧
F
(ω
1
(
x'
)) =
F
(ω
2
(
x'
)),
(1)
where
F
(ω
1
(
x'
)) and
F
(ω
2
(
x'
)) denote results of computing XPath expression
F
(
x'
) by valuations ω
1
and ω
2
, respectively.
Example 6.
Over schema
S
3
(Figure 3), we can specify the following TP-XFD:
F
1
(
x
2
):= /
authors
/
author
/
paper
[
title
= x
2
]/
year
,
(the title of a paper determines the year of its publication), whereas over
S
2
(Figure 3) one of the
following two TP-XFDs can be specified, either
F'
2
(
x
1
):= /
pubs
/
pub
[
title
=
x
1
],
or
F”
2
(
x
1
,
x
2
):= /
pubs
/
pub
[
title
=
x
1
,
author
[
name
=
x
2
]].
Any instance satisfying
F'
2
(
x
1
) must have at most one subtree of the type /
pubs
/
pub
for any distinct
value of
title
(see
J
1
in Figure 2), whereas any instance satisfying
F”
2
(
x
1
,
x
2
) must have at most one
subtree of the type /
pubs
/
pub
for any distinct pair of values (
title
,
author/name
) (see
J
2
in Figure 2).
Further on, we will use TP-XFDs to discover some
missing values
. Thus, we will restrict ourselves
to TP-XFDs determining text values.
Definition 14.
(
text-valued TP-XFDs
) We say that a TP-XFD
F
(
x'
) over a schema
S
(
x
) determines text
values (or is
text-valued
), if there is such
x
∧
x
, that
type
S
(
x
) = type(
F
(
x'
)). Then this TP-XFD will be
denoted by (
F
(
x'
),
x
).
Proposition 1.
(
discovering missing values
) Let (
F
(
x'
),
x
) be a text-valued TP-XFD over
S
(
x
), and
I
=
(
S
(
x
), Ω) be an instance of
S
(
x
) satisfying (
F
(
x'
),
x
). Let ω
1
, ω
2
∧
Ω be such valuations that:
•
ω
1
(
x'
) = ω
2
(
x'
),
•
ω
1
(
x
) =
∧
, ω
2
(
x
) ≠
∧
,
