Database Reference
In-Depth Information
3
Data exchange: key definitions
In this chapter we present formal definitions of the key data exchange concepts that will be
used throughout the topic:
•
schema mappings and source-to-target dependencies;
•
solutions, and the semantics of mappings; and
•
query answering and query rewriting in data exchange.
3.1 Schema mappings
Let R be a relational schema. By I
NST
(R) we denote the set of all database instances over
R. As described in
Section 2.3
, domains of instances come from two disjoint and infinite
sets of values:
•
the set C
ONST
of
constants
,and
•
the set V
AR
of
nulls
, or variables, denoted by V
AR
.
We normally use the symbol
(with subscripts or superscripts) to denote nulls, and low-
ercase letters or specific values to denote constants.
Domains of instances will combine constants and nulls, i.e., they will come from
C
ONST
⊥
V
AR
. Most of the time (but not always) we assume that domains of source in-
stances come from C
ONST
only.
The three essential components of a schema mapping are:
∪
•
a
source schema
R
s
,
•
a
target schema
R
t
,and
•
aset
Σ
st
of
source-to-target dependencies
,or
stds
.
Source-to-target dependencies are typically logical sentences over R
s
and R
t
. We have seen
a number of examples in
Chapter 1
, for instance:
dep
FLIGHT(src,dest,airl,dep)
∀
∀
∀
∀
−→
src
dest
airl
∃
f#
∃
arr
ROUTES(f#,src,dest)
∧
INFO FLIGHT(f#,dep,arr,airl)
.
