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how such knowledge may arise. Each case must be dealt with on its own merits
where the designer supplies the heuristic component.
Techniques for the system to automatically extend the model as the problem
space is explored have had some success in reducing the search space for some
problems (e.g. Truth Maintenance Systems). However, in many cases these elaborate
techniques have had only marginal effects. In the end, it usually falls upon the
designer of the system to incorporate as much domain knowledge as possible in the
heuristic component.
An alternative approach to the search space problem is to use more powerful
computers, and in particular to use parallel processing. It would seem natural to use
parallel exploration of a divergent problem space, but the amount of improvement de-
pends upon the structure of the problem space. The control and intercommunication
of the parallel processes for optimum effect is still a research topic.
The “fundamental” reasons for the slowing of progress call into question many
of the assumptions on which logic and formal systems are based. It is clear from the
description of the general structure of Artificial Intelligence programs that:
1. The concept of truth never enters into the issue of design except as a marker to
show valid deduction,
2. There are several elements that must still be provided by the designer, the
knowledge engineer and the user.
The elements comprising 2 are:
•
The heuristic knowledge and purpose for which the solution is required (the
'heuristic' component).
•
The range of interpretations of the symbols and structure in the model (the
'abductive' component).
•
The association of the distinctions in the world with the primitives for each case
(the 'abstractive' component).
•
The creation of a model from a theory and its subsequent modification in the light
of experience (the 'abductive' and 'inductive' component).
These are similar or associated reasons to those reasons why Wittgenstein explored
an alternative view to his Tractatus and why Peirce concerned himself with semiotics
and abductive inference. Part of the problem can be illustrated by a re-drawing of
Fig.
10.3
as shown in Fig.
10.7
.
Figure
10.7
suggests that the boundaries of first order and second order logic are
restricted to the abstract world and limited to the relationships between theory and its
models. Thus, the range of interpretations is not open-ended. However, there may be
an infinite set of interpretations within each range. The vertical axis in Figs.
10.5
and
10.7
is an ordinal measure of transfinite numbers. The mapping of theory to model
is a second order issue since the theory is used to generate new predicates. In the
slide example, the new predicate Friction (x, f) was implied where x is a body and f
the frictional force.
