Re: Universal mapping of words to integers

As a mathematician I must concur with Enrique. Only for selected domains of discourse is it possible. You will run into problems when trying to come up with a universal system.

If you are familiar with Godel's Incompleteness Theorems (http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems) there are enumeration schemes mapping well formed formulas, such as simple phrases in a language to integers using prime factoring.

Now if you want plain one-on-one mapping Enrique's argument holds, if you want to somehow include semantics, the situation becomes similar the proof construction for the Incompleteness Theorem.

Universality implies completeness and is not possible. But since the semantic web is about making visible linkages in selected domains of discourse, thus limited set of words, there are options available.

 
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________________________________
 From: Enrique Pérez Arnaud <enriquepablo@gmail.com>
To: Michael Schneider <schneid@fzi.de> 
Cc: semantic-web@w3.org 
Sent: Friday, May 18, 2012 10:53 AM
Subject: Re: Universal mapping of words to integers
 

Hi,


2012/5/18 Michael Schneider <schneid@fzi.de>

 
Try this Wikipedia page instead:
>
>   <http://en.wikipedia.org/wiki/Lexicographical_order>
>
>
A mapping of integers to words based on their lexicographical order is only universal for a fixed set of words.  The criteria that the OP offers, if I understand them correctly, neither seem to be intrinsic and exact properties of words, but circumstantial properties.

For a universal mapping, given words formed out of 26 characters, I would go for a base 26 numeration system approach. Of course, no word semantics in the mapping.

-- 
Enrique Pérez Arnaud
enriquepablo@gmail.com

http://npl.readthedocs.org