RE: what is the meaning of the RDF model theory?

The slides

http://www.w3.org/2000/Talks/0906-xmlweb-tbl/slide6-6.html
http://www.w3.org/2000/Talks/0906-xmlweb-tbl/slide7-6.html

are not public.

-----Original Message-----
From: Seth Russell [mailto:seth@robustai.net]
Sent: Wednesday, October 17, 2001 2:36 PM
To: Pat Hayes
Cc: RDF-LOGIC
Subject: Re: what is the meaning of the RDF model theory?


From: "Pat Hayes" phayes@ai.uwf.edu

> >Well let me rephrase:  Being able to ~represent~ the thing inside the
> >computer should be our requirement.
>
> Yes, sure. But now follow through on that thought. There are the
> integers, let us suppose, and we invent a way to represent them in
> the computer, say using base-4 numerals: 0 ,1, 2, 3, 10, 11, 12, ...

I would not say that was ~representing~ the ideal number inside the
computer.  Rather to do that I would put a node (perhaps even a RDF node)
inside the computer and say of that node that it ~represented~ a particular
integer. Here I ~tilde~ the word 'represent' so that you will understand
that I am giving it my particular meaning.  The base-4 numeral strings as
well as the computer's method of operating with those strings could then be
related to that node via some property arc.

> Now we have one thing in the computer which we can define operations
> on, and something else, not in the computer, which that thing in the
> computer is supposed to 'represent'.

Yes.  But the thing we put in the computer is not the ideal number ... nor
is the thing in your mind the ideal number.  That ideal number is something
that both you and the computer can only imagine. You imagine it your way
.... me, my way ... and we could let the computer imagine it with its piddly
little node.  Would that be ok?

>How would we - we humans, who
> are building this thing - describe this whole set-up? Wouldn't it be
> reasonable to talk about the computable representations on the one
> hand, and the (possibly uncomputable) things they represent, on the
> other, and talk about the correspondence between them?

Yes I agree, that would be reasonable.  I want to do that :)

Thing is, if we are desinging RDF for both computers and humans to read and
write, we should (imho) dumb it down such that the computers can compute
whatever is the ~content~ in some reasonable amount of time.

> We might for example say that the numeral '100'
> represents the number 16 in our representation system.

I don't like this narrow way of ~representing~ a number ... probably for the
same objections that you might bring up.

> If you are comfortable with this way of talking, then you are doing
> model theory. That's all an MT interpretation (of a representation
> inside the computer) is: a collection of things that the symbols are
> supposed to represent, and a mapping between the symbols - more
> generally, expressions - and those things. MT just does this in a
> more systematic and general way, is all.

Yes I am comfortable with this way of talking with the substitution of my
~represent~ for your represent.  It is, after all, just the correspondence
theory of truth .. please correct me if that is not so.

>>  If we cannot represent the thing inside the computer,
>> then the computer cannot deal with that thing.
>
> Its not intended for the computer to deal with. It is for us, to help
> us talk about what the computer does.

I was trying to get the computer to understand these things in the same
terms that we talk about them.  I see no reason that we cannot do this,
though it might take a different kind of viewpoint than was possible before
we actually had computers.

>> There are lots of ways to infer things in lots of different kinds of
>> logic. But inevitably they all come down to an algorithm.
>> Represent the algorithm that generates the behavior called
>> inference and you have adequately defined what it means
>> to infer.
>
> Now tell us what it means to infer *correctly*, without somehow
> referring to truth or meaning.

If a mechanism infers some arc which is in contradiction to its axioms, then
it is inferring incorrectly.  How about that?

>> Problem is that if such a theory cannot be represented in the
>> computer, then it is just for the professors and the priests
>
> For any human being who wants to talk and think and theorize
> precisely about his program's meanings. If you don't want to do that,
> then by all means do whatever makes you happier. Some of us do,
> however.

I want to do it too ... I do ... I do.

>> and cannot have any bearing on
>> the behavior of the computer except indirectly through the action of the
>> priests and professors.  Please don't get me wrong and that that as a
>> slight against  priests and professors.  But mathematically I think we
>> can get them out of the loop.
>
> But why would you want to? You ARE one of them.

You flatter me, but I will at least cop to being human ... though you don't
really know that, do you.  The thing that talks from mbox seth@robustai.net
could, for all you really know, actually be an advanced bot.  See,  this
thing that talks from that mbox just loves to play it is a computer .. and
loves to find and employ computers that are good at playing they are human.
So as this technology advances, making that distinction will become very
tenuous indeed.

>> Why anoint just one program?  Why not specify in RDF which
>> interpreter and inference engine applies for each context?
>
> How? That is an infinite regress. If the interpreter defines the
> meaning of the RDF and is itself defined in RDF, where do we start?
> You can bootstrap, but you have to start somewhere.

In this context I did not say 'the interpreter would define the meaning of
the RDF'.  What do you mean when you refer to meaning, anyway?  I seems to
me that your terms are in infinite regress, not mine.  To a computer
operating on an arc in its memory, there is no question what it means ...
only whether the arc is there or not ... or if the arc can, or can not, be
inferred with the axioms and inference engine that apply to that particular
arc.

>> There is no need to define Windows XP as part of the definition of
>> RDF. But we could define a virtual machine interpreter that would
>> function on RDF graphs to define (and manifest) behavior.
>> I know  this is possible.
>
> Sure, but its just as easy (actually easier) to define one of these
> to draw invalid conclusions as it is to draw valid ones, so who is to
> say which one is right? Just behaving doesn't mean that one is
> behaving *correctly*.

We can define correct behavior in relationship to particular sets of axioms
and an inference .. can we not?   I thought that was what logic did. Aside
from that there are many uses of RDF graphs that claim no relationship to
any particular set of axioms and inference engines.  I hope that the RDFMT
will not be running around calling those alogical sets of RDF statements
meaningless.  In fact,  I would hope that this theory would be agnostic as
to the what those statements mean to humans and machines.

>> An interpreter running on RDF type graphs is so simple that even
>> I can understand it.
>
> OK, what does it do if it has two copies of the same graph but with
> the anonymous nodes permuted? Is it allowed to put new names on the
> anonymous nodes if they don't clash with any other names? Justify
> your answer :-)

I can't figure out what you mean by 'nodes permuted'.  But let me have a go
at this anyway ...

If some process knows that two graphs are the same, and if there are
sufficient URI in them to bootstrap the process, then there is some process
which can discover the node to node correspondence between the graphs.  Were
the two graphs to be merged, they would end up being just the one graph.

If an anonymous node is read into a  graph,  and there are ways to infer
that it is the same as an already existing node in that graph, then the
semantic processes that are in charge of keeping the graphs should merge the
nodes.  TimBl gave us a beautiful  mentograph of this ... shuttle back and
forth between the two slides ... you can't miss the point ... note that, per
the graph alone, they are all anonymous nodes:

http://www.w3.org/2000/Talks/0906-xmlweb-tbl/slide6-6.html
http://www.w3.org/2000/Talks/0906-xmlweb-tbl/slide7-6.html

Seth Russell

Received on Thursday, 18 October 2001 11:26:01 UTC