Information Technology Reference
In-Depth Information
Fig. 10.7
The boundaries of first and second order logic
The mechanism through which this generation of predicates occurs is not fully
understood; second order logic is incomplete. It is for this reason that the counterar-
gument that logicians might raise concerning the generalization of logic to include
any number of stages of abstraction cannot be fully justified. The complete formal
step between levels of knowledge has not yet been achieved.
There are two-level 'abductive' programs that incorporate both theory and model
based on something like a simple second-order logic (e.g. Langley et al.
1987
).
Nevertheless, the engagement of the model with the world still requires human action
except in some very primitive cases (e.g. thermostats and other control mechanisms).
The argument for continuing the logic research program is strong and it is not the
purpose of this chapter to suggest otherwise. What is being proposed is that alongside
this research program should be a parallel research program. This program should
include the human agent and a program that attempts to provide a richer structure
to the knowledge description; a structure that can cope with a formal description of
heuristics, interpretation, abduction and induction, a structure that may even be able
to define intelligence unambiguously.
The benefit is not a proposal to develop automated models—that's already
commonplace—but to provide automated aids to the process of moving between
artifact, model and theory. The relationship between artifact and model, and model
and theory is one of generalization and the major limitation of the logic research
program is that by confining its attention to linguistic representations it cannot ad-
equately encompass the full process by which humans move between the particular
and the general. It is not merely the incompleteness (in the logician's sense) of
second-order logic, which stands in the way; it is the incompleteness, in the ordinary
sense, of the representations use by logician's. Here is where there is room to run a
research program alongside the logic program (Addis
1989
).
