- From: pat hayes <phayes@ai.uwf.edu>
- Date: Mon, 10 Sep 2001 20:14:52 -0500
- To: Graham Klyne <Graham.Klyne@Baltimore.com>
- Cc: w3c-rdfcore-wg@w3.org
>>>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. Yes, but if you check the MT for asserted triples, that *is* the meaning of the statement <s p o>. > >>>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. Right. Neat, huh? >? > >>>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. Oh, because another arc can have the same label? Right. I tend to hink of that as a matter of syntax, though. > >(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 hope not :-) > >>>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)". Yes. You can actually derive the property/extension trick by starting with this and thinking of Holds as a (binary) relation between property and the pair (subject,object), and that is then the extension mapping IEXT; so the two ideas are definitely related. (Doesnt work quite the same for more than 3 arguments, though :-) Pat --------------------------------------------------------------------- (650)859 6569 w (650)494 3973 h (until September) phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes
Received on Monday, 10 September 2001 21:13:24 UTC