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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: Mon, 15 Oct 2001 15:26:33 -0500
Message-Id: <p05101006b7f0f1bff85e@[205.160.76.193]>
To: "Wagner, G.R." <G.R.Wagner@tm.tue.nl>
Cc: "'Drew McDermott '" <drew.mcdermott@yale.edu>, "'www-rdf-rules@w3.org '" <www-rdf-rules@w3.org>
>
>    [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.

>    [Pat Hayes] 
>    Rules, in the sense used by the KIF authors, *are* a
>    proof-procedural matter: that is why they are called 'rules'
>    rather than, say, 'implications', you see, and why a notational
>convention has been introduced into the syntax to state
>    them differently.
>
>Sure, the same holds for the concept of a sequent in Gentzen-style
>calculi but still do these sequents satisfy the classical logic law
>of reasoning by cases, and they provide a complete inference
>procedure wrt clasical logic. So, there is no point that rules
>should not respect the law of classical logic just because their
>purpose is to construct proofs.

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.

>    [Pat Hayes] 
>    A rule is invoked only by an assertion. Neither of these rules
>    has a disjunction as an antecedent, so your argument is irrelevant.
>    You are confusing rules with material implications.
>
>I'm certainly not

Well, you seem to be, since under the interpretation you insist on 
imposing on them, 'rules' both have a truth-value in an 
interpretation, and have identical truth-conditions to the material 
implication. I cannot conceive of a closer criterion for identifying 
them.

>(wasn't it me who argued against you that they
>are diferent concepts only recently on this list :-?)

At present in this thread we are arguing over what 'rules' meant in a 
quotation from a document about KIF written a decade ago. In other 
threads on this list we have been discussing what 'rules' *should* 
mean in a yet-to-be-defined extension of a new language. These are 
very different contexts of discussion. In any case, even in the 
latter context, I tried to emphasize that there are two rather 
different senses of 'rule' that we could be discussing, and that one 
of them could reasonably be identified with an implication. And even 
with that identification, there is still the distinction to be made 
between an implication having an antecedent which is true, and one 
that is asserted. As you have pointed out, it is important not to be 
confuse the case where it is known that one of a pair of rule 
antecedents is true, with that of knowing of one of the pair that it 
is true.

>If these rules are supposed to be (non-logical) rules in classical
>logic then they don't need a disjunction in their antecedent in
>order to entail what is entailed in classical logic by the law
>of reasoning by cases.

What you say here makes no sense to me. In my understanding of 
classical logic, rules (in the sense of this thread) do not entail 
*anything*. To speak of a rule entailing something is a category 
error. Sentences entail other sentences, but the KIF quote implies a 
clear distinction between rules and sentences.

>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. To repeat: if you were to identify <= with 
<<=, then all that you say would indeed apply. But the KIF quote made 
this distinction for just this reason, to NOT so identify them.

>It seems to me that this is a confusion

It is not a confusion with anything. It is an extension to the 
language which has a different intended semantics.

>with the negation of
>partial logic where the law of reasoning by cases does not hold,
>and thus '(status-known Joe)' is not entailed, as in logic
>programming. 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.

>Why is it so hard for many people to recognize that classical
>logic is not the proper logic for knowledge representation?

Why is it so hard for people to actually read what other people write?

Pat Hayes
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Received on Monday, 15 October 2001 16:26:36 GMT

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