Re: reification test case

From: "Seth Russell" <seth@robustai.net>
Subject: Re: reification test case
Date: Wed, 6 Feb 2002 12:53:21 -0800

> From: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
> 
> > > > > > > <rdf:description>
> > > > > > > <rdf:type>:Statement</rdf:type>
> > > > > > > <rdf:subject>:Gore</rdf:subject>
> > > > > > > <rdf:predicate>:wonThe</rdf:predicate>
> > > > > > > <log:truthValue>False</log:truthValue>
> > > > > > > </rdf:description>
> > > > > > >
> > > > > > > which holds for all such statings.
> > > > > > >
> > > > > > > But I could also write:
> > > > > > >
> > > > > > > <rdf:description>
> > > > > > > <rdf:type>:Statement</rdf:type>
> > > > > > > <rdf:subject>:Gore</rdf:subject>
> > > > > > > <rdf:predicate>:wonThe</rdf:predicate>
> > > > > > > <dc:author>:Seth</dc:author>
> > > > > > > <log:truthValue>False</log:truthValue>
> > > > > > > </rdf:description>
> > > > > > >
> > > > > > > which holds for a smaller collection of statings.
> 
> > HUH?  How can this be?  The resources above are *resources*, i.e., single
> > elements of the domain.
> 
> The word 'single' is what we are arguing about.  Certainly Bnodes do not
> necessarily refer to a single element of the domain, and nodes of rdf:type
> rdf:Statement are certainly Bnodes.

Bnodes certainly *do* refer to single elements of the domain, as indicated
by the following fragment of the new model theory document:

[[[

<p>Suppose I is an interpretation and A is a mapping from some set
of unlabeled nodes to the domain of I, and define I+A to be an
extended interpretation which is like I except that it uses A to
give the interpretation of unlabeled nodes. Define anon(E) to be
the set of unlabeled nodes in E. Then we can extend the above rules
to include the two new cases that are introduced when unlabeled
nodes occur in the graph:</p>

<center>
<table cellpadding="5" border="1" width="95%">
<tr>
<td>If E is an unlabeled node then [I+A](E) = A(E)</td>
</tr>

<tr>
<td>If E is an RDF graph then I(E) = true if [I+A'](E) = true for
some mapping A' from anon(E) to IR, otherwise I(E)= false.</td>
</tr>
</table>
</center>

<p>&#160;</p>

<p>This effectively treats all unlabeled nodes as existentially
quantified in the RDF graph in which they occur. Notice that since
two nodes cannot have the same label, there is no need to specify
the 'scope' of the quantifier within a graph. (However, it
<em>is</em> local to the graph.) If we were to apply the semantics
directly to N-Triples syntax, we would need to indicate the
quantifier scope, since in this lexicalization syntax the same
bNode identifier may occur several times. The above rule amounts to
the N-triple convention that would place the quantifiers just
outside, i.e. at the outer edge of, the N-triple document
corresponding to the graph.</p>

]]]

If you don't understand the above, you are missing a *vital* point of the
RDF model theory and of blank nodes.


> >There is nothing that I can find anywhere in RDF
> > or RDFS that indicates that any particular resource aside from collections
> > refers to a set of anything.
> 
> Agree, I should have said subclass.

But this doesn't help.  Only classes (resources that are subjs of
statements whose pred is rdf:type and obj is rdfs:Class) can participate in
subclass relationships, and reified statements are not (necessarily)
classes.


> > How can the first resource above refer in RDF (or RDFS) to ``all statings
> > with those three properties which are False''?  There is something that I
> > do *not* understand in your claim above.  Please indicate how you have
> come
> > by this understanding of RDF(S).
> 
> If statings are represented in RDF by Bnodes (and I believe they are), then
> they are just like a KIF  expression
> 
> ((exists ?x)
>      (and (rdf:type :Statement) (rdf:subject :S) (rdf:predicate :P)
>           (rdf:object :O) (.....)  ))
> 
> substitute whatever extra qualifications you want for the (...) .

Well, sort of, but this certainly does *not* make ?x refer to a set or
class or anything but a single element of the domain.  In fact, the above
expression does not make ?x refer to anything in particular.

(You may, instead, be wanting 

      (and (?x rdf:type :Statement) (?x rdf:subject :S) (?x rdf:predicate :P)
           (?x rdf:object :O) (.....)  ))

which could be read, under a variant reading of first-order formulae with
free variables, to mean that ?x refers to an element of the domain that is
a ....  However, again, ?x refers to a *single* element of the domain, not
a set or other collection of elements.

It is true that ?x above can refer to any element with the right
properties, but this does *not* mean that it refers to the collection or
set or group or ....

> > The point is that you seem to be aiming toward the view that there is some
> > difference in essence between the RDF meanings of the two resources just
> > above.  The two things above are just resources, nothing more, nothing
> > less.  They are the subject of several RDF statements (three for the first
> > and five for the second), one of which is given a slight bit of extra
> > meaning by RDFS, but nothing to indicate that there is a type/token
> > distinction between them.
> 
> Could you educate me on the meaning of this term type/token distinction ?

The type/token distinction is either easy (logic) or hard (philosophy).

The easy side is as follows:

The domain of discourse is a collection of objects or tokens.  There are
collections of these objects that form useful groups, which we will call
classes or types.  The two are disjoint.  Tokens have properties.  Types
don't have properties.

The hard side is as follows:

Consider the book example.  A book, like ``Bonfire of the Vanities'', can
be considered to be a token, i.e., a member/instance of the
set/class/collection/type of all books (read as titles).  However, this
same notion can also be considered a type, i.e., the
set/class/collection/type of all physical (paper) books with that title.
Some of the properties of ``Bonfire of the Vanities'', considered as a
type, are also properties of its instances (think of title); some of the
properties of ``Bonfire of the Vanities'', considered as a type, are not
properties of its instances (think of sales figures); some of the
properties of ``Bonfire of the Vanities'', considered as a type, induce or
influence properties of its instances (think of suggested retail value and
actual price).

A physical book can similarly be considered to a token, i.e., a
member/instance of a title.  A physical book can also be considered to be a
type, the type of all manifestations of the physical book, such as being on
the table beside my bed, half-read.  As this is philosophy the above
exercise can be continued indefinitely in both directions.



> Seth Russell

Peter F. Patel-Schneider

Received on Wednesday, 6 February 2002 16:31:28 UTC