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where
F
[
x
] is descriptor dependent with variable
x, a, b, ···, i
are constants. For
descriptor
F
[
x
], if some values of x (
a,b, ···, i)
make
F
[
x
] hold, then we can get
assumption: for all values of
] holds.
(7) Rule transforming conjunction into disjunction
F
1
∧
F
2
::>
K
x
,
F
[
x
|
F
1
∨
F
2
::>
K
(7.15)
where
2
are arbitrary description.
(8) Rule enlarging quantifier range
∀
xF
[
x
] ::>
K
F
1
,
F
|
∃
xF
[
x
] ::>
K
(7.16)
|
∃
xF x
∃
2
[ ]
::>
K
(7.17)
xF x
[ ]
::>
K
(
i
)
(
i
)
1
where
I
1
, I
2
are domain of quantifiers (set of integer), and
I
1
⊆
I
2
.
(9) Generalization decomposition rule
P
∧
F
::
>
K
1
<
F
∨
F
::
>
K
Used in concept acquisition:
(7.18)
1
2
~
P
∧
F
::
>
K
2
Used in description generalization
P
∧
F
∨
~
p
∧
F
|
<
F
∧
F
(7.19)
1
2
1
2
where P is predicate.
(10) Anti-enlarge rule
CTX [
∧
L
=
R
]::
>
K
1
1
<
L
≠
R
::
>
K
[
]
(7.20)
2
CTX [
∧
L
=
R
]::
>
~
K
2
2
where R
1
, R
2
are disjunction expression.
Given an object description which belongs to concept
(positive instance), and
an object description does not belong to concept K (negative instance), the rule
will generate a more general description which includes these two descriptions.
This is the basic idea of learning difference description from instances.
2. Constructive generalization rule
K
Constructive generalization rule can generate some inductive assertion.
Descriptors they used do not appear in initial observation statement, that is, these
rules transform the initial representing space.
(1) General constructive rule
CTX
∧
F
::
>
K
1
<
CTX
∧
F
::
>
K
(7.21)
2
F
¼
F
1
2
