Re: The mentography of reification

From: "Geoff Chappell" <geoff@sover.net>

> My understanding is that the triple can be thought of as defining a
> particular arc in a graph.

Interesting choice of words ... if you will indulge me, I will interleave my
changing understanding of this below.  Pat Hayes has helped with his clear
descriptions  in his recent post to the WG:

http://lists.w3.org/Archives/Public/w3c-rdfcore-wg/2001Oct/0522.html

So the concrete things that exist in time an space are to be called tokens -
and there are many duplicates of those.  The abstract mathematical objects
don't exist in time and space and they are unique.  If you restrain a
collection of tokens to be unique, then you have a set of tokens.  Putting
that restraint on a collection of tokens in a graph is useful because then
the graph is a better match to the ideal mathematical objects.   It still
unclear to me whether we are to call the abstract things 'triples' or
'statements'.  I would prefer the word 'statements' to refer to the things
that exist in space and time and the word 'triples' to refer to the idea
mathematical objects .. but the WG may go the other way.

>That nodes and arcs have identities (locations on
> a page, position in memory, or whatever) and labels.

My understanding is that all nodes have identity internal to a document, but
that only nodes labeled with urirefs have identity outside of the document.
You could  substitute the word 'graph' for document here.   But it is up for
debate whether arcs (triples, arrows) have identity.  RDF M&S says that you
can ~refer~ to them with the reification quad and that internal to a
document you can put an ID on them.  But the WG may change that.

>That with the
> restriction that no two nodes can have the same label, we can uniquely
> identify a node by its label. That with the restriction that duplicate
> triples can not exist, we can uniquely identify an arc by the nodes it
> connects (in order) and the label on the arc.

This is where the confusion between real tokens and ideal objects comes into
play.  I've tried to deconfuse this wrt mentography in a new graph:

http://robustai.net/mentography/reificationDenotes.gif

Note that this graph contains a context called 'ideal reality' which seems
like it should not exist in the graph.  But I used a little trick I learned
from projective geometry where we draw the line at infinity right on the
page ... works like a charm :)   In this graph I also drew some arrows that
seemingly break the rules of mentography ... yet we *can* ~represent~ those
arrows in our graph, we just need to project the ideal reality into the
token reality.

>(Nodes, I guess, are asserted
> into existence by their use in describing an arc?)

Yes definitely: the node itself is a result of a set of arrows having the
same blunt end.

> Taking that view, I'd always envisioned that a nested or reified triple
> would be shown on a graph as arcs originating or terminating on arcs
(though
> I don't know about the validity of that in graph-speak).

Well a token arc cannot terminate on another arc unless you give arcs
extensional identity.  The RDF reification quad gives arcs intensional
identity - it refers to them by criteria ... one might assume then that one
can only terminate an arc on an ideal triple .. but i guess that doesn't
make much sense.  Production [6.12]  of the current M&S might have given
arcs extensional identity within a document ... but the WG will doubtlessly
be changing that.

http://www.w3.org/TR/REC-rdf-syntax/#grammar

Of course mentography and  any application that sits above RDF can make up
its own rules ... I've tried to keep the rules of mentography the same as my
interpretation of the RDF rules ... but the latter seem to be in flux and so
is the former.

But I don't think that nesting relations would ever be an arc terminating on
another arc .. imho it is an arc terminating on a anomous node.  The math
just doesn't work unless you do it that way.  Reifying arcs and nesting
expressions are different things.

>And that the fabled
> statement id is the identity of a particular arc. A quad in that view, I
> guess, is really just a statement that there exists an arc with this label
> and attached to nodes with these labels.

Well that was the best way I thought too, but TimBl pretty much convinced me
that using a context uri would be better.

http://ilrt.org/discovery/chatlogs/rdfig/2001-10-19.html#T17-16-00

> I guess, though, that the idea of drawing sets around nodes and arcs fits
> better with a document-centric (triples in a context) view of the world.
It
> does seem somewhat funny, though, to be enclosing the nodes - it seems to
> imply that their id's are locally scoped.

Yes it does .. and perhaps they are.  If a graph is a real set of tokens
existing in time and space (not an ideal mathematical abstraction), then
(unless we decide to go to a pent and have context and statement id) we will
just have to live with the fact that statements cannot be individually
pointed out.

... thanks for the dialogue...

Seth Russell

Received on Thursday, 25 October 2001 13:10:42 UTC