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Re: Logic and Using The Semantic Web Toolbox

From: pat hayes <phayes@ai.uwf.edu>
Date: Mon, 4 Dec 2000 12:50:15 -0600
Message-Id: <v04210109b6518f1f0349@[205.160.76.86]>
To: Seth Russell <seth@robustai.net>
Cc: www-rdf-logic@w3.org
>"Sean B. Palmer" wrote:
>
> > Yes, I see: TimBL seemed to be implying that logic is inherent to any RDF
> > type system, in fact even more basic that most of the RDF Syntax model
> > itself...
>
>I suppose it depends on what you mean by "logic".   I think RDF (labeled
>directed graphs) entails a commitment to representation, relationship, and
>identity:  hence a commitment to the foundations of language.  But I 
>think there
>is more to logic .... things like the law of the excluded middle come to mind.
>If you look at it from an anthropological perspective, humans must have had
>language far longer than they had logic.   Personally I think this logic stuff
>is far too new to take seriously.

Please don't be offended, but you are making elementary and rather 
silly mistakes here. Look, let's try to use less emotive terminology. 
Instead of 'logic', let us refer to 'content'. The use of language in 
any way (that goes beyond lexicography or the use of fonts for 
decoration) seems to involve the notion of saying something about the 
world; of making a claim about the way things are, by saying 
something about those things. That is what is usually meant by 
'asserting' something; the very idea of 'making an assertion' seems 
to presume that there is some content to the assertion that gets 
made. That is all that is meant by "logic" in the sense being used 
here. Human ancestors have probably had this longer than they have 
had syntax. (Bees have it.) It is intrinsic to the very idea of using 
language to communicate; its the observation that there is more to 
communication than just posting some text somewhere.

One rapidly gets into 'logical' questions, however. If one asserts P 
and also asserts Q, has one asserted the conjunction of P and Q? Is 
it possible to deny one assertion by making a contradictory 
assertion? Is it possible to make an assertion about an entire class 
of things without mentioning them all separately? (As we do by saying 
things like "y'all")  If you can do all that, you already have 
something like first-order logic.

To refer to 'the logic of' an RDF assertion is not to impose any 
*particular* logical rules or contraints on it (like excluded 
middle); it is just referring to the content, and trying to use 
formal tools to analyse it. These are the same tools which are used 
in philosophy of language more generally, and even to analyse the 
meanings of things like diagrams and maps, so there is nothing 
especially left-brained about them, if that is what is worrying you. 
But in any case, RDF is supposed to be machine-checkable, so it had 
better have a reasonably clear formal structure.

The use of these formal (read: mathematical) tools of analysis can be 
useful. For example, RDF appears to not have any negation, so that it 
seems to be impossible to express a contradiction or disagreement in 
RDF. (It is a 'positive' logic.) Tim Berners-Lee *seems* to be saying 
that negation can be defined in RDF by reification. However, it is 
easy to prove that negation canot be defined in a positive logic. So 
either T. B-L is being over-optimistic, or RDF isn't a positive 
logic. But RDF is supposed to be able to express nontrivial content. 
OK, the onus is on the RDF authors to tell us how it manages to do 
this, and especially how this reification-miracle is supposed to work.

(Just to clarify a potential misunderstanding: of course I see how 
the *syntax* of 'not'-expressions might be introduced into the 
language by a reification-type maneoever. But what defines the 
*content* of one of these 'not' expressions, when it is actually 
asserted? The easy theorem in question is that the content of 
negation cannot be defined in a positive logic.)

>Logic is great!  But survival is better :))
>
> > of course this still begs the question:-
> > What namespace do we use for logic assertions, i.e. how can we 
>add it to the
> > basic tenet of RDF?
>
>I thought that was what DAML-ONT was all about.  Isn't it?

DAML is a language which *does* have content. Since it is being 
'built on' RDF, the question arises about what, if anything, that 
'foundation' provides in the way of support for the expression of 
content.

> > A question I am still perplexed by. If this logic is essential to 
>moving RDF
> > to the next stage, why wasn't it built in in the first place, or specified
> > in a satellite draft?
>
>Maybe, perhaps, because it is *not* essential to moving RDF to the next stage.
>I think that the use of RDF for applications that attempt to tame 
>the wilderness
>of the semantic web for use by individuals like you and me will be far more
>important than mere logical inference.

Unless the content of RDF is reasonably clear, it will just produce 
more wilderness. In fact this is already starting to happen. RDF is 
being used in mutually incompatible ways even on this mailing list.

> After all logic sometimes gets us into
>lots of troubles .... ever talk with a binary type person?

Being sloppy about meanings while claiming to have a 'standard' tends 
to produce a lot more troubles, in my experience. But maybe I'm just 
too binary, of course.

Pat Hayes

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Received on Monday, 4 December 2000 13:48:44 GMT

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