
Chapter 8: Intelligent Query Answering
285
JOIN
Let
Tj
and r
2
be two rules defined for relations R and S.
In order to determine the transformability of these rules we have to deter-
mine when the following holds:
r
1
(R)Mr
2
(S)
= r
Q
(RMS)
Let X = Υ Π Ζ be the common set of attributes for R and S. In order for
the above equality to hold, the following necessary and sufficient conditions
must be satisfied:
7r
x
(rj(R))
=
TT
X
(R)
and
ir
x
(r
2
(S))
=
TT
X
(S)
for every R and S (1)
Condition 1 means that rules τ
χ
and r
2
leave the projection on X of R and S
invariant. Indeed, otherwise rules r
t
and r
2
could produce some tuples which
would contribute to the joi ...