From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>

Date: Tue, 23 Oct 2001 14:58:33 -0400

To: melnik@db.stanford.edu

Cc: bwm@hplb.hpl.hp.com, www-rdf-interest@w3.org, simeon@research.bell-labs.com

Message-Id: <20011023145833R.pfps@research.bell-labs.com>

Date: Tue, 23 Oct 2001 14:58:33 -0400

To: melnik@db.stanford.edu

Cc: bwm@hplb.hpl.hp.com, www-rdf-interest@w3.org, simeon@research.bell-labs.com

Message-Id: <20011023145833R.pfps@research.bell-labs.com>

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. 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.) peterReceived on Tuesday, 23 October 2001 14:59:30 GMT

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