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Foundations of Deductive Databases and Logic Programming
book

Foundations of Deductive Databases and Logic Programming

by Jack Minker
May 2014
Intermediate to advanced content levelIntermediate to advanced
752 pages
35h 3m
English
Morgan Kaufmann
Content preview from Foundations of Deductive Databases and Logic Programming
Chapter
2:
Towards
a
Theory
of
Declarative Knowledge
131
So
we
have
/
Ρ
(Α,Τ,φ)
iff
(5)
Β
&M
j+l
for
every negative leaf
Β of Τ
Now, suppose, /ρίΛ,Τ,φ).
By
Proposition
1,
P
J+l
f=A V*i V... VB
k
(6)
where -iB
r
..,
-iB
k
are all and
only
the
negative leaves
of T.
θ,.£Λ/
7+1
(/=1,...,*)
by (5),
M
j+
, f= Λ νβι V... \/B
k
by
Theorem
7 and (6).
Therefore
Λ EM
j+l
.
Conversely, suppose
Α Ε Μ.,.
Then
ΑΕΤ
Ρ
\m(M*),
for
some finite
m.
A routine induction argument shows that there
is an
implication tree
Τ (of
height
< m)
that
is
compatible with Pj
+X
,
has A as its
root,
and has the
property that
Β £ Mj for
every negative leaf
B.
Thus, /
ρ
(Λ,Τ,φ). This com-
pletes
th ...
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Publisher Resources

ISBN: 9781483221120