- From: Graham Klyne <Graham.Klyne@Baltimore.com>
- Date: Fri, 07 Sep 2001 18:43:27 +0100
- To: pat hayes <phayes@ai.uwf.edu>
- Cc: w3c-rdfcore-wg@w3.org
At 07:57 AM 9/7/01 -0700, pat hayes wrote: >>This is something that I have found intuitively "easy" but difficult to >>explain clearly. >> >>My intuition is that an arc is somehow associated with a property node, >>but that different arcs with the same property label are still different >>arcs. (The programmer in me might say that an arc is an instance of a >>type described by the property.) But this is inadequate as a formal >>explanation... > >No, that is pretty good. A relational extension is a set (= class) of >pairs, after all, and each arc is one of those pairs, so is an instance of >the class, exactly. The MT account of this is that every URI denotes one >'thing'; but that when that thing is a property, it has an extension which >is a set of pairs. Every time we write an URI on an arc we are saying that >the pair of things whose names are at the ends of that arc is in the >extension of the thing named by the URI. [...] Neat... I failed to make that step unaided. (In hindsight, I think I should have spotted that from Sowa's description of types logics.) >>It seems to me that there is a difference in the treatment of URIs used >>to label nodes and URIs used to label arcs, but I'm not sure how that is >>formalized. I used to think of reification as providing a way to create >>an effect that might have a graph syntax of an arc pointing to/from >>another arc. > >I don't think you need to involve reification at all; but then I may just >be completely confused about what RDF reification means. I guess the difference is that I saw the arc, the thing pointed to/from, as the statement <s p o>, where taking on board your note above it could be viewed as the pair <s o> in the relational extension of p. >>In any case, I think it's certainly possible to have the uri that labels >>a property arc also be used to label a node that is the subject and/or >>object of another property, which some might say is "to have a property >>be the value of another property". > >Yes, that is OK. No need to change the MT (or the graph syntax) to allow >this. I will put a short note into the MT document to draw attention to this. Let's see if I get it right: a URI used as an arc label, the arc denotes a member of the property node's relational extension. When used as a node label, the node denotes the property itself. ? >>Should arcs be allowed to be "princeNodes"? >> >>I note that allowing property arcs to be "princeNodes" is not the same as >>having ordinary nodes be princeNodes. A URI denotes a node resource, but >>it is an attribute of a property arc. How does a formalization capture >>this kind of distinction? > >Not sure I follow that distinction. ("attribute" ?) I was trying to express that the arc is qualified, not identified, by the label applied to it. (Hmmm... does it make sense to talk of the pair <s o> in the relational extension of p as distinct from an isolated pair <s o>?) >>I have also found that to describe RDF-schema-based inferences, I have >>wanted to construct expressions in which the RDF property is a >>"variable". I think the required effect could be achieved by means other >>than "princeNode" arcs, but maybe less intuitive for a developer. > >Yes, others have noted this also. OK, this also can be allowed in the >syntax without changing the MT; but I think that if we do allow this then >I ought to rewrite the model theory slightly, because as it stands right >now its not quite clear what this would mean. The MT uses a standard >logical device to describe existentials, basically saying that the >existential is true if there is some interpretation of what it denotes >that makes the assertion true. The trouble with this trick for relations >(properties) is, that the simple denotation of a property isn't really all >that important: what makes assertions involving it true or false are the >*extensions* of those denotations. So a lot turns on whether those >extensions are allowed to change when the denotation of the anonymous node >is allowed to change. The only way to interpret this that would produce a >reasonable proof theory would be to take the extension mappings as fixed >and let just the denotations vary; which is what the MT says right now, in >fact, but it ought to say it much more clearly and explicitly, since a lot >hangs on that point if we are going to allow princeProperties. > >>(Hmmm... are we finding out why CGs use bipartite graphs rather than >>labelled arcs?) > >Maybe, but we can go with the more liberal syntax. CGs are based on a >slightly more traditional logic which doesn't have explicit extension >mappings and doesn't allow properties to apply to other properties. I realized later that my thinking there was wrong, in that the bipartite graph's purpose seems to be to allow n-ary relations to be expressed. I think your comment about extension mappings is more to the point. But, having only binary relations may make it easier to introduce the "other means": I was thinking of something like the device "Holds(property, subject, object)". #g
Received on Friday, 7 September 2001 13:55:07 UTC