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RE: Expressiveness of RDF as Rule Conclusion Language (was Re: W hat is an RDF Query? )

From: Wagner, G.R. <G.R.Wagner@tm.tue.nl>
Date: Thu, 11 Oct 2001 14:17:01 +0200
Message-ID: <511BB18E82E9D11188230008C724064602D9DE0D@tmex1.tm.tue.nl>
To: "'tim finin'" <finin@cs.umbc.edu>
Cc: www-rdf-rules@w3.org
> I always liked the example that was given in the KIF documentation 
> (KIF 3.0 Ref. Manual, 
> http://logic.stanford.edu/kif/Hypertext/node37.html):
> 
> ... On the other hand, in some cases, replacing <<= by <= would be 
> semantically unacceptable. For instance, the rules
> 
>   (<<= (status-known ?x) (citizen ?x))
>   (<<= (status-known ?x) (not (citizen ?x)))
> 
> allow us to infer (status-known Joe) only if one of the sentences 
> 
>   (citizen Joe),  (not (citizen Joe))
> 
> can be inferred. Replacing the rules by implications would make 
> (status-known ?x) identically true."

But according to classical (2-valued) logic, there is no difference
here between the rules and the corresponding implications. The 
sentence (status-known Joe) could also be inferred from the 
two rules alone, since every classical (i.e. total and coherent) 
model of the two rules would satisfy it, simply because it would 
either satisfy (citizen Joe) or (not (citizen Joe)), and in both
cases, as it satisfies both rules, it would also have to satisfy
(status-known Joe).

So, the author of this text on KIF seems to make a mistake here.
In fact, he unintentionally describes the behavior of rules in 
extended logic programs where "not" corresponds to the strong 
(monotonic) negation of partial logic, where models are partial 
and the "tertium non datur" (= law of the excluded middle) does 
not hold.

-Gerd

---------------------------------------
Gerd Wagner  
http://tmitwww.tm.tue.nl/staff/gwagner/
Dep. Information & Technology 
Eindhoven University of Technology  
Email: G.Wagner@tm.tue.nl 
Phone: (+31 40) 247 26 17  
Fax: (+31 40) 247 26 12 
Received on Thursday, 11 October 2001 08:17:05 GMT

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