12
Quantifier Rank
•
The
quantifier rank
of a formula
f
is
defined inductively:
qr(t
1
= t
2
) = qr(R(t
1
,…,t
n
)) = 0
qr(
f
1
Æ
f
2
) = max(qr(
f
1
), qr(
f
2
))
qr(
9
x.
f
) =1+qr(
f
)
etc
•
FO[k] = all formula
f
s.t. qr(
f
)
·
k