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RE: problems with concise bounded descriptions

From: <Patrick.Stickler@nokia.com>
Date: Sun, 3 Oct 2004 16:37:52 +0300
Message-ID: <1E4A0AC134884349A21955574A90A7A50ADD04@trebe051.ntc.nokia.com>
To: <tshipley@deru.com>
Cc: <www-rdf-interest@w3.org>

> -----Original Message-----
> From: ext Trent Shipley [mailto:tshipley@deru.com]
> Sent: 02 October, 2004 00:09
> To: Stickler Patrick (Nokia-TP-MSW/Tampere)
> Cc: www-rdf-interest@w3.org
> Subject: Re: problems with concise bounded descriptions
> On Friday 2004-10-01 08:12, Patrick.Stickler@nokia.com wrote:
> > > -----Original Message-----
> > > From: ext Benja Fallenstein [mailto:b.fallenstein@gmx.de]
> > > Sent: 01 October, 2004 17:43
> > > To: Stickler Patrick (Nokia-TP-MSW/Tampere)
> > > Cc: pfps@research.bell-labs.com; www-rdf-interest@w3.org
> > > Subject: Re: problems with concise bounded descriptions
> > >
> > >
> > >
> > > Hi Patrick, hi Peter--
> > >
> > >
> > > I believe that there are at least two general problems 
> that Peter has
> > > with the specification. First, the much discussed paragraph:
> > >
> > >      A concise bounded description of a resource is a body of
> > > knowledge
> > >      about that resource which does not include any 
> explicit knowledge
> > >      about any other resource which can be obtained
> > > separately from the
> > >      same source.
> > >
> > > Aside from the details you've discussed, the more fundamental
> > > issue is
> > > that Peter sees this as a *definition* of CBD: i.e., 
> everything that
> > > fits this description is a CBD.
> Sorry, I haven't been following this closely.  I am going to 
> try to produce a 
> more rigorous statement of the definition.

Great. I'll do what I can to help (with the caveat that
I am not a mathematician, which should be obvious to most
by now ;-)

> Resource: undefined
> Body of Knowledge: undefined
> Explicit knowledge: undefined
> Given a resource R[a] (a named set) and
> Given Body of Knowledge K[a] (a set)
> Then a Concise, Bounded Resource Description [sic] is defined as:
> R[a], such that the contents of R[a] contain K[a] 
> AND all elements of K[a] are about (that is, reference) R[a] 
> (or objects in 
> R[a]).

Hmmm... my understanding of the above would seem to include
triples where the resource is the object (i.e. arc-in triples)
which are not included in CBDs, except in the case of anonymous
nodes which might refer back in some way to the resource that
is the focal point of the description.

> Furthermore:
> Let  K[a'] be a subset of any explicit knowledge in K[a] 
> (call this e(K[a])) 
> where K[a'] references any member of the set not-R[a] 
> (written ~R[a]) or any 
> contents of ~R[a]. 
> Then e(K[a]) includes no K[a']
> =================
> But that is as far as I get because the phrase "separately 
> from the same 
> source" could be interpreted as referring to EITHER R[a] or 
> ~R[a] (though 
> intuitively R[a] seems the better candidate.

Take as given that

1. A CBD is a subset of a specific RDF graph (= "source")

2. Extraction (or identification) of that subset begins at
   a particular node in the graph, which denotes the resource
   of interest.

Does that help you continue?

> ===============
> Note also that the fragment:
> <quote>
> R[a], such that the contents of R[a] contain K[a] 
> AND all elements of K[a] are about (that is, reference) R[a] 
> (or objects in 
> R[a]).
> </quote>
> Would seem to define a set of knowledge rather than a 
> resource _per se_, 

Well, a CBD is a body of knowledge about a particular
resource denoted by a particular node in a particular
graph, so if your attempting to define a CBD as other
than a set/body of knowledge that that could be a

> namely K[a] bounded by R[a].  K[a] is not necessarily a 
> proper resource, but 
> only implicitly a resource (that is we could give K[a] a 
> name, that is a 
> proper, explicit reference). The definition also has no 
> content defining 
> "concise" like requiring K[a] to be finite or in some sense minimal.  
> We can think of other potential set algebraic properties that 
> a bounded 
> knowledge set, K[a] might have that could prove interesting.  

Certainly. Those that have been identified in various
discussions about CBDs, both recent and past, include

- the original definition of CBDs, with no reference to
  inverse functional properties, as implemented by the
  present deployment of the Nokia Semantic Web Server

- inverse functional bounded descriptions, per the current
  CBD document 

- symmetric versions of either/both of the above, which
  would additionally include triples where the node
  in question occurs as object

I'm considering a revision/reworking of the CBD document
to address the various comments recently raised, as well
as to clarify the relationship/boundaries of that document
to more general query interface/API issues, and to identify
alternative/derivative forms of descriptions which may
also be found useful to particular applications.

> (For now we 
> forget about conciseness, since the original definition 
> actually included 
> nothing about conciseness like K[a] is finite, or K[a] is a 
> minimal spanning 
> set.)

Well, I think it needs saying that I do not intend to apologise
for or change my choice of words in the materials I have 
written, because they are written in *ENGLISH* not mathematics,
and if some particular term happens to have a special, precise,
narrow meaning to mathematicians that does not mean that others
are not free to continue to use that term per its other (often
far longer and more traditional) meanings when they are not
purporting to present some idea in formal mathematical terms.

So if I use the words "explicit", or "concise", or "definition",
or any other word, and anyone is unclear about what I mean by
those, I suggest they consult Webster's dictionary or any
similar dictionary of standard English usage.

I do, however, welcome the assistance of anyone having the
interest, and ability, to provide more formal, mathematical
definitions of these ideas. 

But I will not apologise for having "misused" any particular
term because I have not used it in a way compatible with some
precise, narrow, specifically mathematical sense.

(and sorry if "precise", "narrow", or "specific" also have
any mathematical sense where the above use will confuse).

Received on Sunday, 3 October 2004 13:39:48 UTC

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