
Chapter
2:
Towards
a
Theory
of
Declarative Knowledge
117
Proof:
Straightforward—use the bubble sort. •
We now complete the proof of Theorem 11. Let ß
p
...,ß
w
and
Q\,...,Q'
n
be two stratifications of Ρ consisting of clusters. If the relative order of two
clusters Q
i
and Q. in these two sequences differs, then by Lemma 12 Q
i
and Q-
are unrelated. Then by Theorem 4, T
Q
and T
Q
are independent. This together
with the previous lemma concludes the
proof.
•
An
Alternative Characterization
of M
p
The definition of the model M
p
is somewhat operational in the sense that it is
defined in terms of the iterations of the operators T
p
. We now offer another,