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RE: Expressiveness of RDF as Rule Conclusion Language (KIF or not to KIF)

From: Pat Hayes <phayes@ai.uwf.edu>
Date: Tue, 16 Oct 2001 13:35:27 -0500
Message-Id: <p0510102bb7f22c523ca8@[205.160.76.193]>
To: "Wagner, G.R." <G.R.Wagner@tm.tue.nl>
Cc: www-rdf-rules@w3.org
>  > >    [Gerd Wagner]
>>  >    Notice that we can associate a model-theoretic semantics with
>>  >    rules in a natural way: an interpretation satisfies a rule
>>  >    (is a model of it) if it satisfies its consequent whenever it
>>  >    satisfies its antecedcent.
>>  >    ... using the above definition of a model of a rule, we can
>>  >    define that a rule set R entails a sentence F
>>  >    if all models of R satisfy F.
>
>>  >    [Pat Hayes]
>>  >    However, that is not the way that the KIF authors are intending
>>  >    to use the term 'rule'
>>  >
>>  >But then they have a somewhat strange understanding of rules.
>>
>>  It evidently does not correspond to yours. It is, however, one that
>>  has a long tradition in some academic circles, and to which the KIF
>>  authors were referring.
>>  ...
>>  I do not have either the time nor the inclination to argue this case
>>  with you, as there is really nothing useful to argue about. The point
>>  at issue is that there is a sense of 'rule' which was being used by
>>  the KIF authors that does not correspond to your understanding. That
>>  does not mean that they were making a mistake, however.
>
>You seem to suggest that he above model-theoretic characterisation
>of rules is just my private opinion,

It is one that I personally have not previously come across in quite 
this form, I confess.

>and that it is no problem (e.g.
>for KIF) to ignore it. This is not the case! Such a model-theoretic
>treatment of rules is kind of folkloristic and also used in logic
>text books.

No doubt. But folklore depends on who your folks are. Many AI workers 
number among their kin people who work on rule systems that have no 
connection to logic whatsoever, such as production systems. They also 
use the terminology of 'rules' and 'pattern' and 'trigger' and 
'invocation' and so on, and many of them wouldn't know a model theory 
if it bit them in the ankle. They do not even think of these rules as 
having anything to do with making assertions; they think of them as, 
if anything computational, simply a kind of distributed process 
description.

>  > >You may intend them to be used in an
>>  >incomplete inference operation, but as I have argued above,
>>  >why would you want that we miss certain valid conclusions
>>  >that could be drawn if we just 'repair' the inference engine?
>>
>>  Maybe it was never broken.
>
>If you say "broken" then you should be able to tell me with
>respect to what semantics? Or do you identify the semantics
>with the particular inference engine chosen here?

If you were to say 'virtual machine', I might be willing to do that, 
yes. The particular inference engine is not really germane to the 
point at issue; the distinction between truth and assertion is 
germane, and that can be described at a level of abstraction somewhat 
above the details of any particular inference scheme.

>
>>  >So, apparently, KIF wants to stay at the "safe"
>>  >side (classical logic) while at the same time it wants to use
>>  >a negation that is more intuitive and cognitively adequate than
>>  >classical negation. But such a balancing act is not possible!
>>
>>  Seems easy enough to me. Use two negations, for example.
>
>That's exactly what we have in (extended) logic programs.
>But it's no longer classical logic!

KIF is not classical logic, then, in your very strict sense. It 
includes classical logic, however, rather than being a restriction of 
it.

Pat Hayes
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Received on Tuesday, 16 October 2001 14:35:29 GMT

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