Re: namedNode? in predicate position?

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