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RE: NPR, Godel, Semantic Web

Title: RE: NPR, Godel, Semantic Web

> -----Original Message-----
> From: Thomas B. Passin [mailto:tpassin@home.com]
> Sent: Monday, May 07, 2001 6:01 PM
> To: xml-dev@lists.xml.org
> Subject: Re: NPR, Godel, Semantic Web
> In Semantic Web inferencing - notice that that is the term
> usually used -
> we're
> 1) not talking usually about deduction but inference, perhaps
> with degrees of trust or certainty,

Can somebody clarify the difference?

> 2) not normally talking about stepping outside the area of
> normally-used logic to apply some meta-logic (third order logic??).

I don't claim to know much about this area, but it's not
obvious to me that:

"Is every phone number in Poughkeepsie, NY to be formatted with the rules for the USA?" and "Is every even integer expressible as the sum of two primes?" have different orders of "meta-ness". 

The first is a Semantic Web use case I remember from somewhere, and the second is Goldbach's Conjecture, a (possibly) "true but unproveable" assertion often used as an example of a "Gödel sentence." 

Maybe it's because the domain of Golbach's conjecture is much greater than that of phone numbers, locations, and formatting rules. Gödel's theorem applies in axiomatic systems rich enough to contain arithmetic.  Could it be that the "semantic web" as an axiomatic system will not be rich enough to contain arithmetic, but could be rich enough to perform any practical inference of use to us?  That seems counter-intuitive, at least if you think of "common sense" as an incredibly intricate web of assertions and inference rules.  Maybe it's only the size of the "semantic web" that matters rather than the "richness" of its axiomatic system?

Again, I don't claim to understand, just posing questions in hopes of making sense of this stuff.