interpretations and identifications

I was worried that David and I might have different ideas of what the  
group's charter or plan was, so I tried to figure out where we agreed  
or disagreed. The below is obviously my own distorted memory... my  
apologies to David if I've misrepresented him.

1. We agreed that the charter is to publish an ontology of some kind

2. We agreed that if it got to the point where we were forced to  
decide between OWL DL and N3 (with rules), that would represent success.

3. We agree that RDF and/or OWL formal semantics are fundamental.

3a. We didn't agree whether RDF/OWL were informed or constrained  
somehow by "web architecture". I maintained that they weren't, that  
you can conform to RDF semantics without having any respect for "web  
architecture". Quoth Hayes [1]:

"The semantics does not assume any particular relationship between the  
denotation of a URI reference and a document or Web resource which can  
be retrieved by using that URI reference in an HTTP transfer protocol,  
or any entity which is considered to be the source of such documents.  
Such a requirement could be added as a semantic extension, but the  
formal semantics described here makes no assumptions about any  
connection between the denotations of URI references and the uses of  
those URI references in other protocols.

The semantics treats all RDF names as expressions which denote. The  
things denoted are called 'resources', following [RFC 2396], but no  
assumptions are made here about the nature of resources; 'resource' is  
treated here as synonymous with 'entity', i.e. as a generic term for  
anything in the universe of discourse."

I believe it's the intent in both RDF and OWL semantics to cut the  
cord with the web, and that this is a good thing.

3b. We didn't agree on how RDF might inform web architecture. This  
hinges on the relation between "denotes" and "identifies" (in the  
webarch sense).

Remember that an interpretation is an assignment of things  
(mathematical, real-world, or otherwise) to URIs. A model theory says  
what it means for a given interpretation to be a model of an axiomatic  
system. Web architecture says (in its inimitable way) what it means  
for a given interpretation to agree with what it calls "identifies" -  
one might call such an interpretation a model of web architecture or a  
model of webarch identification.

There are many legitimate reasons why conformance to constraints -  
whether logical or not - may be unspecified or underspecified. A set  
of constraints never specifies a unique model, even in the simplest  
mathematical situation, or with the most well-crafted prose.

I would say that "denotes" is a general term to be used for any  
constraint system, and should only be used either when the system is  
specified (in context) or aggressively unspecified (as in, say, RDF  
semantics). I would not want to nail it down to any particular  
interpretation, given that there may be may be many interpretations of  
a system under analysis.

Because it's so useful the way it is, I'd reserve "denotes" for the  
general metatheory case, not tied to webarch or Euclidean geometry or  
anything else, and use "identifies" (not a term I like, but following  
Harry's suggestion to follow webarch) specifically in the theory of  
web architecture. In a model of webarch, a URI will be said (in its  
theory, in RDF) to identify what it denotes (in its metatheory,  
expressed in mathematical prose), but in a model of something else, it  
won't.

We have become accustomed to using "denotes" with web architecture, in  
part because it's superior in many ways to "identify".  But how would  
you document it then?  You can't talk about the interpretation,  
because that lives at the metalevel - this would be circular. You  
could define it to be webarch identification, but then why did you  
change the label? "Denotes according to an interpretation specified as  
follows: ..." -- then how do you fill in the ...?

I'm not seriously proposing that we talk about models of webarch, just  
introducing the idea to explain myself.

4. I proposed we *not* do any metamodeling at this point, meaning that  
there should be no URI in the ontology for "denotes", "models", etc.,  
as this risks being circular, even if we can figure out which  
interpretation is meant. David disagreed, saying that otherwise we  
don't know what RDF we're working with, or what URIs in general mean.  
I said let's just assume for now that have a ready supply of it, and  
work instead on figuring out what it would mean, if we had it. There's  
plenty to do before we get blocked for want of a formal metatheory of  
axiom set synthesis and denotation.

(OK, now to hope that Pat doesn't give his pupil's essay a bad grade.)

Jonathan

[1] http://www.w3.org/TR/2004/REC-rdf-mt-20040210/

Received on Wednesday, 4 February 2009 16:37:22 UTC