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From: rbl@nitrex.UUCP ( Dr. Robin Lake )
Newsgroups: sci.lang,comp.ai
Subject: Re: Infinite alphabets - (Turing via Berke)
Message-ID: <557@nitrex.UUCP>
Date: Thu, 15-Oct-87 13:53:56 EDT
Article-I.D.: nitrex.557
Posted: Thu Oct 15 13:53:56 1987
Date-Received: Sun, 18-Oct-87 00:00:02 EDT
References: <154@Aragorn.UUCP> <114400001@exunido.UUCP> <364@su-russell.ARPA> <17@krafla.UUCP> <8583@shemp.UCLA.EDU>
Reply-To: rbl@nitrex.UUCP ( Dr. Robin Lake )
Organization: The Standard Oil Co., Cleveland
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Xref: mnetor sci.lang:1573 comp.ai:909

In article <8583@shemp.UCLA.EDU> berke@CS.UCLA.EDU (Peter Berke) writes:
>
> ...
>This is also the intuitive reason I claim ambiguity resolution 
>is not computable.  I think of ambiguity resolution as the
>general case of "object recognition" and "problem formulation." 
>Imagine a vague scene or situation not already described by a finite
>enumeration of the objects in it and their relationships, etc.
>Such a vague scene is equivalent, in Turing's sense, to supposing
>an infinite number of things in the scene, which you are going to reduce
>to a finite number of options from which to choose.  Since you are
>supposing an infinite alphabet (or the equivalent "vague" scene) technically,
>you are not computing.  
>
>  ...
>
>Peter Berke


"Computable/Computing" with the current mathematics.  If you go back to the fundamentals
of math (Robinson's axiomatic set theory) and remove the Axiom of Choice, one
can derive a new mathematics which is more appropriate for situations where
uncertainty prevails.  This line of reasoning has worked extremely well in
developing some powerful tools for "smart" data analyzers where the data is
too dirty and uncertain for classic statistical techniques.

-- 
Rob Lake
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