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In-Depth Information
12.2.2
The Inductive Process
The inductive process is the qualitative assessment of the abduced hypothesis set
against pre-defined criteria (Chap. 11, Table 11.1). These criteria are primarily
concerned with determining whether the hypothesis is simple enough to warrant
acceptance. The set of criteria employed for this validation are the obvious features
such as size of representation (it must be within a certain threshold value), param-
eters should be rational, the level of differential depth should not exceed a certain
limit, etc. The criteria selection for assessing the abduced hypothesis is governed by
the inverse of learning employed in retroduction. We employed a probability density
table (as in retroduction) to keep track of the history of selection of criteria for each
hypothesis and a criteria probability table to keep records of occurrences of criteria.
The rule for updating the probability density table is similar to P(Ci|Fj) above:
H
j
)=
p(H
j
|
Cr
i
) P(Cr
i
)
P(H
j
)
P(Cr
i
|
where
n
p(H
j
)=
p(Cr
j
|
H
i
) P(H
i
)
i=1
The calculated
a posteriori
probabilities of each criteria in the density table, P(Cr|H),
are used to calculate the determinant of the criteria D(Cr
i
) for the abduced hypothesis
using:
n
D(Cr
i
)=
log P(Cr
i
|
H
j
) log P(H
j
)
j=1
All non-zero D(Cr
i
) are taken to be the criteria to be assessed. If an abduced hypothesis
matches all these criteria, it is an acceptable hypothesis. Otherwise, the retroductive
process takes control and creates a new hypothesis as a function of the next concept
in the ranking.
12.3
Feedback Assessment
Before the actually inductive assessment is carried out, there is a feedback assessment
carried out. Feedback assessment looks for “irregularities” in the abduced hypothesis.
These “irregularities” are used to refined a hypothesis to fit important criteria of
acceptability. For example, given a function:
x
4
16x
3
96x
2
f(x)
=
−
+
−
256x
+
256
from a sequence (256 81 161011681256
...
.), the deductive process will detect
that the retroduced function consists of fairly large numbers. The criteria indicate
