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From: jfox@netcom.com (Jeff Fox)
Subject: Re: THEOREM-PROVER in FORTH wanted (based on LAWS OF FORM)
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Date: Wed, 11 Dec 1996 21:15:25 GMT
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In article <2087@purr.demon.co.uk> jack@purr.demon.co.uk (Jack Campin) writes:
>
>Laws of Form is a pretty trivial system (there is an article in Notre
>Dame Journal of Formal Logic from the late 70s that gives a precise 
>characterization of it - basically a weakened Boolean logic) and there
>should be no big problem in finding a no-worse-than-NP-complete-or-
>thereabouts proof system for it. There wouldn't be a whole lot of *use*
>in such a tool, though; LoF simply doesn't express anything worth beans.

In the forward to Laws of Form Bertram Russell said that he felt that
Brown had provided a simple way to represent fundamental concepts
that for the first time tied together some different fields of
mathematics.  
I know two math professors who always argue about whether the
approach is worthwhile.  I was not interested in its use in
formal mathematics, but for engineering and AI.
When people ask "what can you do with the Laws of Form?" I think
it no different than asking "what can you with math?"
Chuck thought that the representation of feedback in electronic
circuits as imaginary numbers was interesting and said he might
use it in CAD some day.
Other companies have been using programs based on lof to reduce
the complexity of circuit designs.
I have always been more interested in using laws of form as a
shorthand representation for logic in natural language and problem
solving as detailed in appendix II.   I like he way it can represent
paradox, and I think it may provide a very efficient way to deal
with some of the classic problems with AI.
I have given a couple of talks about the design of these programs
and have had some encouraging feedback.  One math professor said
that this approach might be like the use of 0 in mathematics.  The
number 0 doesn't seem like much in itself but without it many
things are much more difficult and with it many things are much
easier.  And like the number 0 the Laws of Form is an attempt to
find something very basic but widely applicable.
We are normally taught math in a way that reflects more historic
tradition than planned stages of concepts.  Rather than starting
with the laws of calling and crossing and then proceeding on
through boolean logic and non-numeric arthimetic we jump in at
numeric arithmetic.  Buy the time people have had ten or twenty
years of exposure to increasingly complex concepts in math they
sometimes have difficlty seeing that there are things that are
simpler and more fundamental than 1+1=2 and can't see that these
things might be valuable fundamental concepts.
I was exposed to lof before Forth, but always saw many parallels
after I learned Forth.  Many people see Forth and say "Ahah, I
see the big picture and the beauty of the simplicity."  Many
people see Forth and say "Nothing that simple could have any value."
I have seen the same thing with lof only longer.  I also quite
frankly don't understand all the arguments that I have heard
against lof, but I have always suspected that part of the
problem is that to see a basic concept that you didn't see
decades eariler requires accepting that you might have missed
something.  I have sometimes asked people "What did you hear
Chuck say?" after one of his chats.  "Well he said that I was
an idiot for using C."  If Chuck said "I have found a superior
solution." this implies to some people that if they didn't
find a superior solution that they are inferior, and since they
cannot accept that they conclude that Forth is not worth beans.
But I am more interested in results than in theory, and in fact
don't have an interest in formal mathematics.  I don't see how
lof can be a miss for what I want to do with it.  I am far more
intested in a way to find a shortcut to results rather than a 
proof that the process was "logical."  This was IMHO the biggest
problem with classic AI.  Classic AI was crippled by formal logic
in a world where one must deal with paradox.  Mathematitions and
classic AI programmers like proofs but it has very little to do
with the way people think.

Jeff Fox

