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Re: a new way of thinking about RDF and RDF Schema

From: Sergey Melnik <melnik@db.stanford.edu>
Date: Tue, 23 Oct 2001 14:18:49 -0700
Message-ID: <3BD5DEB9.D53C3A51@db.stanford.edu>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
CC: bwm@hplb.hpl.hp.com, www-rdf-interest@w3.org, simeon@research.bell-labs.com
"Peter F. Patel-Schneider" wrote:
> 
> From: Sergey Melnik <melnik@db.stanford.edu>
> Subject: Re: a new way of thinking about RDF and RDF Schema
> Date: Tue, 23 Oct 2001 11:50:35 -0700
> 
> > "Peter F. Patel-Schneider" wrote:
> > >
> [...]
> > > Pat's RDF graphs don't handle order.  However, it is possible to, and has been
> > > done (but my reference is at work), add order to a graph that represents
> > > RDF and XML information.  There are lots of ways to do this, one would be
> > > to add a partial order over edges.
> >
> > Well, how do you squeeze the partial order information into the graph?
> > I'm not asking for academic reasons. Ordering is a critical feature for
> > many applications, and if there is no adequate way of introducing order
> > into RDF "as is", we may have to rethink the basics of the RDF model
> > (sooner or later). So please let me/RDF Core know about your ideas once
> > they are in shape...
> >
> > Sergey
> 
> Harold Boley has a data model, at
> http://www.dfki.uni-kl.de/~boley/xmlrdf.html, that uses total
> orders over some of the edges coming out of a node.  This has a
> disadvantage when considering multiple ``XML'' documents.  However, it is
> an interesting way of proceeding.

Thanks for the pointer, I'll have a look.

> Another way, as I said above, is to add a partial order over edges in the
> RDF graph.  This would result in something like:
> 
> An untidy RDF graph, R, is a four-tuple (that can be considered to be a
> partially node labeled, edge-ordered, directed triple-graph)
>                 < N, E, LN, EO >
> where N is the set of nodes in the graph
>       LN :(partial) N -> URI u L gives labels for nodes
>       E <= N' x N'' x N is the set of edges in the graph
>         where N' = { n : LN(n) is undefined or LN(n) in URI }
>         where N'' = { n : LN(n) is defined and LN(n) in URI }
>       EO is a partial order over E, i.e., a subset of E x E that is
>          transitive and irreflexive
> 
> Now the edge order is only used to order the edges that come out of a node,
> so you could also add a condition on EO that edges with different heads are
> incomparable or make EO map nodes into partial orders over pairs.
> 
> Interpretations then have to be augmented with something like
> 
> An interpretation I is a four-tuple
>         < IR, IEXT, ICEXT, IO, IS >
> where IR is a non-empty set, called resources
>       IEXT : IR -> powerset ( IR x (IR u LV) )
>       ICEXT : IR -> powerset ( IR u LV )
>       IS : URI -> IR
>       IO : IR -> powerset ( (IR x (IR u LV)), (IR x (IR u LV)) )
>         such that IO(r) is a partial order
>         and if IO(r) contains <s,o> < <s',o'>
>             then <s,o> in IEXT(r) and <s',o'> in IEXT(r)
> 
> The notion of a model also has to be extended, perhaps by
> 
> 4. for <s,p,o> < <s',p,o'> in EO, <M(s),M(o)> < <M(s'),M(o')> in IEXT(M(p))
> 
> (Actually this would probably work better using a <= version of a partial
> order, to take care of special cases.)

This is an interesting way to go. Is there a way to introduce ordering
in some generic fashion say by using reification? As you noticed, there
are many ways to state ordering, e.g. order of edges by
subject-predicate, or just by subject, or by object etc. All these ways
seem valid and useful... For example, I may want to state that objects
of property dc:creator (authors) are ordered, and conversely, the
subjects are ordered too (ordered list of books authored by an
individual).

Sergey
Received on Tuesday, 23 October 2001 17:05:53 GMT

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