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C00002 00002	logic[f86,jmc]		Mathematical logic and artificial intelligence
C00003 00003	Mathematical Logic and Artificial Intelligence
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logic[f86,jmc]		Mathematical logic and artificial intelligence
-for Daedalus

sentences as propensities to behave

a different view of some philosophical issues comes from taking AI
seriously - the design stance.


Mathematical Logic and Artificial Intelligence

	The idea of using mathematical logic as the basis for
artificial intelligence can be said, in a generous interpretation,
to go back to Leibniz.  He proposed to express the facts about
the world in a form of mathematical logic that was yet to be
invented and to settle arguments about facts and policies by
calculation.  Unfortunately, Leibniz did not succeed even in
inventing propositional calculus, which had to wait for Boole
about 150 years later, who in turn didn't invent predicate
calculus.  Leibniz's failure to invent propositional calculus
requires an explanation, because he was the co-inventor with
Newton of the infinitesimal calculus, which is mathematically
far more complex.  The explanation, I think, is that we humans
find understanding our own mental processes very difficult,
and progress is slow.  This applies to our own time, as well
as to Leibniz's.  I'll conjecture that when mental processes
are well understood, the explanation won't be deep, and the
scientists of that time will have difficulty explaining why
we missed what then seems obvious.

	There are two different approaches to the project of
understanding mental processes --- the biological view and
the mathematical view.

	The biological view is that mental
processes are a biological phenomenon, mainly observable in
humans, and that the essence of their study is to determine
how they are carried out in humans.  The main criterion for
judging a proposed intellectual mechanism is whether there
is evidence that it is indeed used by humans.
In particular  we must ask what evidence there is
of the extent to which humans use anything like mathematical
logic in deciding what to do.

	The contrasting mathematical view is that
mental processes are concerned with deciding what to do
as it depends on the structure of the world, the structure
of information available and how more information can be
obtained, and the structure of goals to be achieved.  As such
artificial intelligence is basically a mathematical problem.
For example, if only our goals consisted of minimizing a
linear function in the presence of linear constraints, then
artificial intelligence would be coextensive with the theory
of linear programming.  In fact the information structure
of the common sense world is quite different from those
amenable to classical mathematical treatment, and entirely
new methods have to be developed.  The major criterion for
proposed intellectual mechanisms is how well they work, and
in today's practice the main problem is that all presently
understood methods are too specialized.

	This paper takes the mathematical view, even omitting
discussion of the strong interaction between
the two research programs --- finding out how humans solve
common sense problems and devising good ways of solving them.

	(McCarthy 1960) proposed the following.

<quote if there is a concise one>


Remarks:

generality problem

blocks world and general motion axiom

context problem

elaboration tolerance

It is not my objective in this article to engage in controversy,
but I should certainly mention that controversy exists.  Perhaps
when I see the other articles, I'll regret this decision.

use of logical formalism to express facts
	ad hoc programs for reasoning
	answering questions
	achieving goals