# 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>

```>  > 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
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
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 UTC

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