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Re: Predicates and Arcs vs Triples RE: use/mention and reification: rdf:predicate/subject/object

From: Graham Klyne <GK@ninebynine.org>
Date: Thu, 31 May 2001 12:56:31 +0100
Message-Id: <5.0.2.1.2.20010531114733.0305bab0@joy.songbird.com>
To: pat hayes <phayes@ai.uwf.edu>
Cc: www-rdf-logic@w3.org
I've been mulling your response, on and off, for a couple of days.  I think 
I'd like to take your points out of order, as the second part may shed 
light on the first...

>>I view "arcs and nodes" (as in directed labelled graphs) and "triples" as 
>>different presentations of what is fundamentally the same syntax.
>
>I would respectfully suggest that you might want to re-think this 
>identification; or at least, that you distinguish *syntax* from 
>*structure*. A single structure can encode a variety of different 
>syntaxes, but the logical semantics needs to have the actual syntax to 
>attach to, not its implementation structure.

You are right that I have not been clear about "syntax" vs "structure":  I 
had been treating syntax as a kind of structure.  If I interpret you 
correctly, "structure" refers to some way of constructing information 
composites from component parts (lists, arrays, sequences, tuples... even 
triples).  Syntax, on the other hand, describes a a set of rules for 
construction of valid sentences;  thus, a syntactically valid sentence has 
not only some surface form, but an associated parse tree - to which the 
semantics might be attached.

Am I on track so far?

I had thought I was treating graphs and triples in the syntactic sense when 
I made the claim above.  But I'm beginning to see that the syntactic 
structure of just triples is too simple to provide hooks for meaningful 
semantics.

I think you may be saying that, in order to attach meaningful semantics, 
certain values or sets of values that appear within the triple structure 
must be recognized as distinguished symbols in the syntax, in order to be 
able to say that they have specific associated semantics.

For example, for "reification" to be at all workable as a mechanism for 
attaching new semantics to RDF graphs, the properties and classes that are 
used by reification must be recognized as distinct syntactic symbols with 
specific syntax productions governing their use.

So, to defend my original statement above about the equivalence of "arcs 
and nodes" and "triples", I should have described them has "fundamentally 
the same structure".  Or I could choose to view them as the same syntax, 
but that would be a syntax that is fundamentally too primitive to serve as 
a basis for any useful semantics.

At 11:41 AM 5/29/01 -0500, pat hayes wrote:
>>At 01:52 PM 5/27/01 -0400, Jonathan Borden wrote:
>>>This argument is oft stated. And in the early days of software, similar
>>>arguments were made regading the lack of ability of a high level language to
>>>express anything beyond what is expressed in machine language.
>>
>>That is very different from the argument I am advancing.  I am saying 
>>that triples are something in which the various "high level languages" of 
>>resource description might be grounded, and (assuming adequate semantics) 
>>through which the various forms of "high language may" be related.
>
>Let me home in on this. A problem, I think, with a lot of this discussion, 
>is that words like 'grounded' and 'related' are used without being clearly 
>defined. There is certainly one sense in which any notation can be 
>'grounded' in triples, or represented as triples, since any graph can be 
>encoded as a collection of triples. OK, let us agree on that. And these 
>structures can be used to encode all of the syntactic forms of  various 
>"high-level" languages, which can be provided with suitable semantics, 
>presumably. All of that is uncontroversial.

Yes.  But I had hoped that "grounded" might be a stronger idea.  See my 
final comments below.

>  The heat is generated when one tries to fit these together. The RDF 
> model tries to attach the semantics directly at the triples level, which 
> forces it to use reification as a kind of universal syntactic solvent.

Aha!  In consideration of the first part above, I think I see a chink of 
light here.

>   That is what some of us find an unacceptable trade-off, as it uses a 
> huge burden of semantic expressivity (KIF is probably the only formalism 
> on the planet with a fully defined truth predicate, and even that has 
> never been used in practice by anyone, as far as I know, and is likely to 
> be eliminated from the new KIF standard) to purchase a tiny advantage in 
> interoperability (the property that any set of triples is well-formed.) 
> Also, we are pretty sure it is going to lead to problems later: it is 
> notoriously easy to produce paradoxes if used casually, it renders any 
> 'genuine' usage of reification semantically suspect, and so on.

... but now you've lost me.

In other messages, I've tried to explore the possibility of using 
"reification" to achieve some stated goals *without* requiring a truth 
predicate.

What I'm taking from this exchange is the possible idea that this cannot be 
done based on the syntax(sic) of triples alone.  For this one needs (at 
least) a richer syntax that, if encoded in triples, recognizes special 
combinations of triples, such as "reification" and others, as distinct 
syntactic constructs.

>>[...]
>>> >
>>> > I think their is a fair community investment in the triple form, and that
>>> > it should not be discarded unless we are certain that it is fundamentally
>>> > inadequate.
>>>
>>>I submit that the community investment is in _arcs and nodes_ not triples
>>>per se.

I think the investment is in both.

In view of the above comments, I would suggest that the "interesting" 
challenge here may be to devise an abstract syntax for RDF that *can* be 
encoded in arcs+nodes/triples/XML in a way that is consistent with current 
implementations of RDF applications.

...

I don't think I've said anything significant above that hasn't already been 
said by you or others.

But something that exercises me is the possibility that there might be a 
"basic RDF", complete with model theoretic semantics, that corresponds 
approximately to Existential-Conjunctive (EC) logic [1], and one or more 
"extended RDF"s that share the same EC-based semantic foundation, even 
though they add different semantics on top.  Roughly, this would mean that 
any RDF expression that used only the EC subset would be interpreted 
equivalently by different "extended RDF" systems.

Why do I think this is an interesting, maybe useful idea?
(a) it provides a common, simple basis for representing ground facts, and 
exchanging them between systems.
(b) it is very simple to implement for applications that don't need to do 
any more than interpret ground facts.
(c) I have a hunch that it is compatible with the use of RDF by many 
current applications.

#g
--

[1] There are several references to Existential Conjunctive logic on John 
Sowa's book "Knowledge Representation".


------------
Graham Klyne
GK@NineByNine.org
Received on Thursday, 31 May 2001 08:14:31 GMT

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