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

From: Pat Hayes <phayes@ai.uwf.edu>
Date: Thu, 11 Oct 2001 18:24:59 -0500
Message-Id: <p0510100db7ebd60858af@[205.160.76.193]>
To: "Wagner, G.R." <G.R.Wagner@tm.tue.nl>
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.

Why not? The 2-valued status of the logic says nothing about how to 
interpret *rules*. That is the point being made by the KIF authors: 
one is not obliged to consider a rule as meaning the same as an 
implication. An implication is an assertion in the language; an rule 
is a licence to perform an inference. The deduction theorem in 
classical logic shows that they are closely connected, in that the 
implication (implies A B) is valid (true in all models) just when the 
rule (from A infer B) is also valid (ie when A entails B); but this 
is simply a fact about the semantic relationship between  an 
expression and a rule. It does not create any kind of imperative that 
any deductive processor must obey every rule, particularly if the 
corresponding implication is not valid.

Sometimes, one can utilize a restriction on a rule to convey the 
presence of more information than could be inferred using the 
implication alone, as is obviously intended in this case by the use 
of 'status-known', which seems to convey the meaning of something 
being provable rather than simply true. KIF is richly endowed with 
meta-descriptive abilities which make such usages quite natural to 
contemplate.

>The
>sentence (status-known Joe) could also be inferred from the
>two rules alone,

 From the two implications, but not from the rules. In fact, strictly 
speaking, nothing can be inferred *from* a rule, only *by* a rule.

>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).

(I think you mean, as it satisfies *one of the* rules?). But merely 
being satisfiable in a single interpretation is not sufficient to 
trigger a rule.

>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.

No, that is not correct. For some reason, you are denying the obvious 
point being made here, and then going on to draw inappropriate 
conclusions from your misapprehension. The very point being made is 
that a rule need not be understood as an implication, so there is no 
need to deny the tertium.

Pat Hayes

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Received on Thursday, 11 October 2001 19:25:07 GMT

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