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Re: New RDF model theory (well, damn nearly)

From: Frank Manola <fmanola@mitre.org>
Date: Sat, 18 Aug 2001 18:34:28 -0400
Message-ID: <3B7EED74.402@mitre.org>
To: pat hayes <phayes@ai.uwf.edu>
CC: RDF Core WG <w3c-rdfcore-wg@w3.org>
Pat--

You wrote:

 >PS. Frank, I still havnt considered the issue you raised about rdf 
 >vocabulary having to have an 'associated' schema, because I
 >now realise I have no idea what it means, or at any rate how it would 
 >effect the semantics. (Suppose there wasn't an >'associated' schema? 
 >What RDF graphs would change in meaning? )

I think this "associated schema" business is not as precisely expressed 
as it might be in the M&S, but the following musings try to convey the 
general idea I had in mind (and we can possibly take this discussion as 
an example of using the model theory to clarify what the specs ought to 
say or not say).  I don't think any of this will be unfamiliar to you, 
since DAML is based on the same idea, and I don't think the DAML model 
theory covers this issue explicitly either (so maybe it's inappropriate 
in a model theory).  Anyway:

Background:

As I said in my original message, there are various places in the M&S 
that tie property names to specific schemas:

*  p60 says "Property names must be associated with a schema."  It then 
goes on to say that this can be done by qualifying the names with a 
namespace prefix to identify "the corresponding RDF schema" [admittedly 
a *syntactic* mechanism].

*  Section 2.2.3 further discusses the idea that the meaning of a 
property name will be pinned down by associating it with a particular 
schema.  In particular, p85 says "Meaning in RDF is expressed through 
reference to a schema."  [Hence the relationship with semantics].  This 
paragraph also muddies the waters a bit by saying "A variety of schema 
forms can be used with RDF, including a specific form defined in a 
separate document [RDFSchema]..."

The general idea, then, is that people will identify the intended 
interpretation of the property names they use by defining a schema 
containing them, along with associated definitions and constraints that 
reflect (to the extent the schema capabilities allow) that intended 
interpretation (that intent can be documented "more meaningfully", as 
far as computer processing is concerned, by using more powerful 
languages, e.g., DAML+OIL vs. RDFS, but that's something of a separate 
issue).  The reference to a schema distinguishes a particular property 
name from the same name used with a different meaning by somebody else, 
possibly defined in a different schema.

My original thought, specifically due to sentences like "Meaning in RDF 
is expressed through reference to a schema", was that this seemed like 
something that ought to be reflected explicitly in a model theory of RDF.

Development:

Going through the model theory (especially before you added coverage of 
RDFS), I think I see what you mean about this not necessarily having any 
effect on the semantics.  [Interpolation:  your question "Suppose there 
wasn't an 'associated' schema? could on one hand be answered by saying 
that it's syntactically irrelevant:  the M&S says there must be an 
associated schema.  However, the question needs to stay on the table, 
because it may be something that the M&S doesn't need to say, or needs 
to say in some other way.]  That is, as far as the RDF graph is 
concerned, properties are URIs, are thus unambiguous, and have the 
meaning of the associated resource (in the case of properties, 
presumably the meaning attached to the resource by whoever created it). 
  This is reflected in the MT by the URI to resource mapping (for 
resources that are properties).  The semantics would be essentially 
unaffected even if whoever created and used a property didn't explicitly 
document the meaning they had in mind for it anyplace (problems might 
arise if there was a need to share that meaning with anyone else, but 
we're not talking about that yet.)  Taking this line, the reference to 
an associated schema is just a way of saying that there is a need for 
some *syntactic* mechanism to allow RDF writers to universally identify 
a specific property, and referencing a schema provides a way to do that.

On the other hand, there remains this idea, mentioned above, that people 
will try to describe the intended interpretation of property names by 
defining schemas.  The schemas may contain additional information about 
the property resources identified by property URIs (like constraints, 
which constrain the valid instances of the property).  This seems 
clearly related to the semantics of the associated graphs.  The intended 
usage is that people will define schemas that reflect their intended 
interpretations for the RDF they write, and then write the RDF.  The RDF 
will be indirectly asssociated with its semantics via the reference to 
the schema.  Now, this isn't universal, in the sense that it covers all 
the RDF that may be written.  For example, even if there were an RDF 
schema that you and I explicitly refer to in exchanging information, we 
could also have some "side agreements" where we use additional terms, 
not reflected in the schema, whose meaning only you and I knew and 
agreed to.  However, a general idea in RDF (and more extended Semantic 
Web) usage is that meanings will be grounded by associating terms with 
schemas (or, by extension, ontologies).  What I was after was something 
in the model theory that explicitly reflected this idea.  I haven't yet 
digested your MT section on RDFS interpretations enough to tell if there 
is anything along these lines in there (is there?), so this response may 
be premature (or just laziness on my part;  asking you to tell me, 
rather than figuring it out for myself!).  It seems to me that there 
might be something, for example, that explicitly tied the 
interpretations of the classes and properties defined in the schema to 
the interpretation of, e.g., those properties when used in the graphs. 
It seems to me that the situation we have here is somewhat different 
from the situations in which model theories are used in "vanilla" FOL, 
in that here we have some explicit definitions in schemas (and 
ontologies) that attempt to, if only very partially, specify or 
constrain the intended meaning of the names that are used, and that 
somehow the model theory should somehow reflect that "role" that the 
schemas are trying to play in defining the meaning of associated graphs. 
  Does this make any sense?

--Frank

-- 
Frank Manola                   The MITRE Corporation
202 Burlington Road, MS A345   Bedford, MA 01730-1420
mailto:fmanola@mitre.org       voice: 781-271-8147   FAX: 781-271-875
Received on Saturday, 18 August 2001 18:34:29 EDT

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