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From: ucacpaf@cs.ucl.ac.uk (Alasdair Turner)
Subject: Re: How to remove underpants (Was FIRST order?)
Message-ID: <ucacpaf.807187881@cs.ucl.ac.uk>
Date: Mon, 31 Jul 1995 10:51:21 GMT
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A.Sloman@cs.bham.ac.uk (Aaron Sloman) writes:

>[...]
>Is it possible to remove the underpants without removing the
>trousers (i.e. the waistband of the trousers remains constantly
>around the person's waist), allowing only continuous changes of
>shape of the legs and underpants e.g. stretching, bending, twisting,
>but no separation of anything into disconnected parts, no creation
>of new holes, etc.?
>[...]

>g. Can the methods that people use be implemented on digital
>   computers?
>
>h. If not, what classes of mechanisms suffice to support those
>   methods of reasoning? (Compare building a 3-D rubber model and
>   manipulating it. Is that any less a reasoning process than
>   writing formulae on paper and manipulating them?)

(a bit of weak AI...)

Well, when thinking about it, I visualised the movements of legs,
underpants, etc.  Which leads to a stick model similar the rubber model
that you suggest.  If you can codify the stick model then you can formalise 
the problem (hmm).  Perhaps some sort of graph would suffice.  The rules of 
the game seem fairly straight forward.  It looks rather like a game of chess 
to me, each move altering the state of the system, a game plan to remove the 
underpants.  Only in this game the physical constraints may be changed (e.g.,
very short legs, extrememly baggy underpants and so on).  Hence...

>d. What would the knowledge actually look like if expressed in some
>   form of predicate calculus, or other logical system?
>     (I.e. which predicates, functions, etc. would be used? which
>     axioms? Would modal operators be needed? Is higher order logic
>     needed to express the constraint that everything that starts
>     connected remains connected throughout? Would temporal
>     operators be needed to express the notion of a process and the
>     constraints on the process? How would the requirement that the
>     waistband not be moved be expressed? How would the initial
>     state and desired end state be described?)

...rather like a program to play chess?  Hence...

>f. Can the problem be solved using logic (first order? higher
>    order?) and if so what would the proof look like (I'd love to
>    see a logical proof of the possibility of removal).

...why not (it might take a while: think how long it's taken computers to 
master chess)?  Surely the problem is not that we can't write the logic to
describe the problem, but rather that we can't write the logic to write 
the logic to describe the problem.

>Maybe this problem could be adopted as a nice challenge for AI?
>(I am not trying to prove that AI is impossible. I am trying to
>help define its objectives.)

I don't know, it really does seem to me that we can write a chess program
for many problems.  Just as we can write infinitely many fuzzy logic systems
for an infinite number of less well defined problems.  

As I've said, this doesn't seem to solve the problem of how we set about to
write the logic in the first place.  (This seems a fairly obvious statement:
have I misinterpretted the question?)

Paf Turner 

http://www.cs.ucl.ac.uk/staff/A.Turner  A.Turner@cs.ucl.ac.uk
Department of Computer Science, University College London, UK.

