Information Technology Reference
In-Depth Information
Table 11.1
Criteria for induction
Criteria
Meaning
CR1
The size of the hypothesis representation should not exceed a certain threshold value
CR2
All parameters used in the formulation of a hypothesis should be in integer form
CR3
The length of coefficients is set 1
CR4
All parameters are rational numbers
CR5
All coefficients are less than or equal to 10 and greater than or equal to
−
10
from which to generate a hypothesis (see Table 12.1 in Chap. 12). The process
of hypothesis generation can be expensive and therefore a good initial choice of
hypotheses will improve the potential success. However, this choice is in some sense
making a pre-judgment and is in competition with induction. Learning in induction
is the selection of a criterion from a set of criteria that relates to each concept. It is
interesting to see that both the learning processes are complementary to each other
to achieve symmetry. The learning in induction (the validation of a concept) is the
inverse of learning in retroduction (the generation or selection of a concept).
There are two kinds of learning used in retroduction. The first kind of learning
is a simple training set to establish a norm from which insight may be gained. This
enables the system to orientate towards generally humanly accepted hypotheses as
opposed to workable but humanly unacceptable hypotheses. The second kind of
learning uses the facts given (e.g. the number sequence) in order to do a running test
of confidence between competing hypotheses. We test both mechanism of learning
over the same set of data in order to compare the relative changes in performance.
11.4
The Basic Concepts
This model employs five basic quantitative concepts to act as hypothesis generators.
The concepts are shown in Table
11.2
.
The five concepts can be recognized by the way they are formed.
11.4.1
INTER
This is a relationship between an element S
i
in the sequence S and with those
preceding it.
A
i
∗
S
fi
i
−
1
+
S
i
=
k
i
For a particular sequence the start value, A(i), f(i) and k(i) need to be determined in
order to fit this function.
