Re: RDF Investigations

On Jun 23, 2013, at 11:49 AM, Gregg Reynolds wrote:

> Hi folks,
> 
> A couple of years ago I got the idea of finding alternatives to the
> official definition of RDF, especially the semantics.  I've always
> found the official docs less than crystal clear, and have always
> harbored the suspicion that the model-theoretic definition of RDF
> semantics offered in http://www.w3.org/TR/rdf-mt/ was unnecessary, or
> at least unnecessarily complicated.  Needless to say that is my own
> personal aesthetic judgment, but it did motivate my little project.
> 
> I guess the past two years have not been completely wasted on me; what
> was a somewhat vague intuition back then seems to have matured into a
> pretty clear idea of how RDF ought to be conceptualized and formally
> defined.  Clear to me, anyway; whether it is to others, and whether it
> is correct or not is a whole 'nother matter.
> 
> Since pursuing this idea will involve a lot of writing I won't pursue
> it here; instead I've described the the basic ideas in a blog post at
> http://blog.mobileink.com/.

Hmm. You say some things in there that seem to be just plain wrong. 

1. [The RDF semantics] "restricts interpretation to a single semantic domain." 

I am not sure how you can possibly read the semantics in this way, but the whole point of model theory is to permit many - usually, infinitely many - interpretations, over arbitrary domains. The only domain restriction in RDF (as in most model theories) is that the domain be non-empty and that it contain basic literal values such as character strings. 

2. "The so-called abstract syntax described  in RDF Concepts and Abstract Syntax serves as the formula calculus, but it is incomplete.  It specifies that a triple (statement) "contains" three terms (nodes), and that an RDF graph is "a set of triples".  But these are not rules of a calculus; they do not tell us how to construct statements in a formal language."

First, the whole point of defining an 'abstract' syntax is to allow for a variety of concrete (lexical) syntaxes, so if you prefer to work at a concrete level, just choose one of those, eg RDF/XML or N-Triples. But more to the point, the abstract graph syntax *is* a formal language with a perfectly well-defined syntax. It is not a character-string syntax, but it is a syntax, with exact syntactic rules. A very simple syntax, but that simplicity was a deliberate part of the design.

3. "... semantic entailment (not to be confused with logical entailment)..."

Can you elicidate what you see as this distinction that is not to be confused? The textbook account of a formal logic distinguishes entailment, a purely semantic notion, often symbolized by the sign |=, from deducibility (via formal inference rules and axioms, typically), often symbolized by |-, and completeness is the property of these two coinciding. I do not know of any notion of logical *entailment* other than the semantic |= notion. Deducibility is not entailment. 

4. "The business of model theory is to build a bridge between formal calculi and (informal) semantic domains.  You don't need a formal representation of the semantic domain..."

Model theory *is* the result of formalizing the semantic domain. That was the new idea in Tarski's original publication which founded the subject in the 1940s. HIs title, you might recall, was "A theory of truth for formalized languages".

5.  "...model theory, ... makes automated proof a legitimate idea." 

Proof theory makes automated proof a legitimate idea. Model theory establishes completeness of the formal proof methods. 

and I guess I won't bother to go on with this list.

Your main point, however, seems to be that one could formalize RDF as an uninterpreted calculus and then go and look for alternative ways to interpret it, and maybe find some new ones. I am sure that this program would succeed, in the sense that you would indeed find alternative semantics. But let me ask the larger question: what exactly is the point of this enterprise? Since the only point of inventing RDF in the first place was to provide for a basic degree of interoperability at a semantic level, what purpose could there be in ignoring this aspect of RDF? Considered as a pure, uninterpreted formal calculus, RDF is hardly there at all, it is so minimal. As you point out, it does not come with any proof rules or indeed even with any notion of proof already defined for it, and if you don't think the graph syntax is adequate, then it doesn't even come with a syntax. So it is hardly there at all: no wonder you could, if you were so inclined, make it into just about anything at all, if you ignore the normative semantics. If you want to have fun with formalisms, why not choose something with a bit more bite to it, such as an uninterpreted lambda-calculus, say? Or Javascript? 

>  The allusion to Wittgenstein, that great
> philosophical therapist, is entirely intentional.  You (or at least I)
> find out a lot of things when you analyze a concept very closely; if
> my analysis is not mistaken, there are some fundamental problems in
> the land of RDF.  For example, it is possible to show, among other
> things, that the concept of a graph is not essential to RDF; nor is
> the treatment of the Property node of a triple as an arrow or relation
> necessary; nor is the concrete semantics defined in the RDF Semantics
> document the only or even the best "theory" of RDF.

If you can give up on all this, what do you take yourself to be referring to when you say "RDF" ? You have just dismissed virtually every defining characteristic of RDF as either wrong or inessential. So what is left? 

Pat

>  (Maybe this is
> all obvious to the cognoscenti, but insistence that RDF just is a
> graph is very common.) On the positive side, thinking about RDF as a
> mathematical domain (or domains), independent of RDF as a language,
> leads to a pretty substantial improvement in clarity; and since it
> requires a certain amount of creativity it's just fun.
> 
> The reason I'm posting this here is because I will need some help,
> especially from real mathematicians and logicians.  A category
> theorist, for example.  Not only to check my reasoning; my hope is
> that others interested in pursuing this line of thought might come up
> with yet other fresh ideas.
> 
> Plus, I've had a lot of fun thinking along those lines, and since a
> lot of people on this list spend a lot of time thinking about RDF
> (among other things), I thought they might find it interesting and fun
> as well.  The plan is to post a series of blog articles fleshing out
> the ideas in coming months, so if anybody would like to help or
> collaborate please let me know.
> 
> Cheers,
> 
> Gregg Reynolds
> 
> 

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Received on Monday, 24 June 2013 14:32:52 UTC