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5. While LE( e i ,+ x ) = no, for positive example set + x ,or
6. LE( e i ,- x ) = yes, for negative example set - x ,
7. i i + 1;
8. Output e i .
7.9.2 Model inference
A model inference problem is an abstraction from scientific problems. In this
abstraction we try to find some unknown model M which can explain some
results. Shapiro gave the following definition of the model inference problem.
Suppose that a first order language
and two subsets of it, an observational
language Lo , a hypothesis language L h , are given. In addition, an oracle for some
unknown model M of L is given. The model inference problem is to find a finite
Lo
L
. In order to solve the model inference problem,
Shapiro has developed a model inference algorithm in terms of Gold's theory
(Shapiro, 1981).
-complete axiomatization of
M
L
sentence is divided into two subsets: observable language
Lo
and
hypothesis language
L h . Assuming that
'
Where is empty sentence. Then model inference problem can be defined as
follows: given one-order language
L o Ք
L h Ք
L
L
and two subsets: observable language
L
o and
hypothesis language
L h . Further, given a handle mechanism oracle to unknown
model
M
of
L
, model inference problem is to find a definite
L o of
M
completed
axiomatization.
Algorithm to solve model inference problem is referred to as model inference
algorithm. Enumeration of model M is an infinite sequence F 1 , F 2 , F 3 , , where
F i is the fact about
M
, each sentence α of
L o is taken place at fact
F i
= <α,V>,
i
>
0. Model reasoning algorithm reads a enumeration of observable language
L o
once. A fact which generates definite set of sentences of hypothesis language
L h
is referred to as speculation of algorithm. A kind of model inference algorithm is
as follows:
Algorithm 7.13 An enumeration model inference algorithm (Shapiro, 1981).
1. Let
h
be a total recursive function
false to { }, S true to {}, k to 0
3. Repeat
4. read the next fact
2. Set
S
F n =<α,V>
5. add α to
S v
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