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.cb REPLIES TO COMMENTS ON "FORMALIZING OCKHAM'S RAZOR"
Reply to A.P. Acosta
The usual model building in operations research or economics or
other social science is carried out by people rather than by computer
programs. It is usually carried out informally on the basis of intuition
or judgment about what is relevant. Circumscription is a formalization of
the reasoning that confines attention to a subcollection of the facts and
assumes the non-existence or non-interaction with the problem of objects
whose existence is not implied by these facts. Whether knowing about
circumscription or other forms of non-monotonic reasoning will help in
this process is like the question of whether other kinds of formalism
help a person doing an intuitive operation. When we consider making
a computer create a model by selecting relevant facts, then the formalization
embodied in circumscription or some other form of non-monotonic reasoning
becomes essential. I don't presently have realistic examples of the
application of non-monotonic reasoning to scientific model building.
Reply to N. Dalkey
1. Universe of discourse is somewhat vague to me, but I'll
do the best I can. It seems to me that the collection of common
sense knowledge available to a scientific model builder does not
correspond to a universe of discourse, because it admits the existence
of entities he hasn't thought of. Similarly, we may imagine collecting
knowledge in a computer in the form of a large collection of sentences
and perhaps other data bases described by sentences, and we may
suppose that this doesn't necessarily constitute a universe of
discourse either. Circumscription and other forms of non-monotonic
reason would have to be used by a computer in forming a universe
of discourse if it was going to use mathematical models of the
kind most scientists consider. However, it is not excluded that
some reasoning might be done without formulating a universe of
discourse. I will again express nervousness about whether "universe
of discourse" has a precise meaning.
2. It seems to me that the rule of always using the narrowest
feasible class A to estimate a conditional probability P(B|A) is
indeed an example of non-monotonic reasoning. We humans are always
doing non-monotonic reasoning. Now we must teach it to computers.
Reply to M. Intriligator
1. Non-monotonic reasoning has both positive and negative
virtues. It doesn't do creative thinking, but it avoids the
requirement of choosing a narrow model before beginning the reasoning
process, and a process that uses non-monotonic reasoning can use
non-monotonic steps tentatively. It provides a formal tool for
restricting attention to the relevant aspects of a problem, but
the heuristics required to use it intelligently still must be
developed.
2. I would be surprised if human non-monotonic reasoning
were especially associated with the division of the brain into two
halves. No simulation of the divided brain seems to indicated in
trying to make computers do non-monotonic reasoning. Non-monotonic
reasoning is being developed as a tool to overcome some of the
limitations of present artificial intelligence programs.