Databases Reference
In-Depth Information
4 Undefinability of Particular Quantifiers
There are the following examples of important 4ft-quantifiers:
•
4ft-quantifier
⇒
p,Base
of founded implication defined in [2] for 0
<p
≤
1
and
Base >
0 by the condition
a
a
+
b
≥
p
∧
a
≥
Base
!
p,α,Base
of lower critical implication defined in [2] for
•
4ft-quantifier
⇒
0
<p
≤
1, 0
<α<
0
.
5and
Base >
0 by the condition
a
+
b
i
p
i
(1
a
+
b
p
)
a
+
b−i
−
≤
α
∧
a
≥
Base
i
=
a
•
4ft-quantifier
⇔
p,Base
of founded double implication defined in [3] for
0
<p
≤
1and
Base >
0 by the condition
a
a
+
b
+
c
≥
p
∧
a
≥
Base
•
4ft-quantifier
≡
p,Base
of founded equivalence defined in [3] for 0
<p
≤
1
and
Base >
0 by the condition
a
+
d
n
≥
p
∧
a
≥
Base
•
Fisher's quantifier
∼
α,Base
defined in [2] for 0
<α<
0
.
5and
Base >
0by
the condition
i
n−k
r−i
min(
r,k
)
n
≤
α
∧
ad > bc
∧
a
≥
Base
i
=
a
+
•
4ft-quantifier
p,Base
of above average dependence defined in [11] for 0
<p
and
Base >
0 by the condition
∼
a
a
+
b
≥
a
+
c
a
+
b
+
c
+
d
∧
(1 +
p
)
a
≥
Base
•
The 4ft-quantifier
→
conf,sup
corresponding to the “classical” association
rule with the confidence
conf
and the support
sup
[1] defined by the
condition
a
a
+
b
≥
a
n
≥
conf
∧
sup
All these quantifiers are classically undefinable. We will prove it for 4ft-
quantifiers
!
⇒
p,Base
of founded implication,
⇒
p,α,Base
of lower critical impli-
