Re: Grist for layering discussion


>  > [pfps:]
>>  1/ All RDF syntax is also RDFS syntax.
>>  2/ Given an RDF information base, i.e., an information base created using
>>     only the syntax in RDF, the RDFS retrieval mechanism produces everything
>>     that the RDF retrieval mechanism would produce, and maybe more.
>>  This is precisely what it means to be an extension.
>That's an extension of functionality and sort-of of the output
>synxtax, like when your bank statement now includes extra information
>to help you compute your taxes.

I wonder if I could interject here. I think it is bad rhetoric to use 
this sort of 'everyday' example, because they all are taken from 
transactions between human beings, and are therefore fundamentally 
misleading at exactly the place where the semantic problems arise. 
The relationship between RDF and RDFS that Peter was describing is 
NOT like ANYTHING printed on a bank statement, or in a book, or on a 
webpage, or said by someone to someone else. It is a relationship 
between formal systems.

>  The input syntax and/or the API have
>not been changed.  Okay.
>>  However, RDF and RDFS have a very uncommon relationship because they also
>>  share a syntax.  Let's try to create a same-syntax extension of RDFS to
>>  encompass some of propositional logic, namely the part that allows us to
>>  create related disjunctions such as John is either married to Susan or
>>  friends with Jake.
>>  [Why do this extension in particular?  Well it is an extension that shows
>>  some of the problems, but it also has a construction that can be fairly
>>  naturally expressed as triples.]
>>  What doesn't work is to directly encode the missing logical
>>  construction.  A direct encoding of this would be something like
>>  IB1	John rdfo:or _:x .
>>	_:x married Susan .
>>	_:x friend Jake .
>>  We construct a formal specification of RDFO to incorporate this
>>  construction.  In particular, from
>>  IB2	John rdfn:or _:x .
>>	_:x married Susan .
>>  RDFO retrieval will produce
>>	John married Susan .
>>  Now is everything OK?  NO!  There are two problems:
>>  1/ Because RDFO is an extension of RDFS RDFO retrieval will also produce
>>	_:x married Susan .
>>     from IB2.  In fact, every RDFO disjunction also creates several
>>     extraneous consequences. 
>>     Well you might argue that the
>>	John rdfn:or _:x .
>>     consequence is benign because it mentions the special RDFO property.
>>     However, the other consequences do not mention any special RDFO
>>     properties and they are definitely not benign.  RDFO has failed in its
>>     goal of capturing related disjunctions.
>Right.  Clearly that was a bad design.  The exact design principle
>violated here I have not seen clearly stated, but it's important.  I
>think TimBL didn't see this problem when he started n3 logic, which
>makes it kind of broken in this same way.  But I believe he does
>understand it now.   We usually talk about it in the realm of
>open/closed world and "that's all their is",

That is a different issue. Don't get them confused. The 'that's all' 
problem is to do with how to encode finite structures in purely 
descriptive format. [The honest answer is that it can't be done 
(because of the second recursion theorem), but there are ways to hack 
it if your tastes run to hacking.]  But that has nothing (directly) 
to do with the central issue being talked about here, which is that 
when you DO describe the syntax, you are making assertions that are 
different from what that syntax was making.

>but perhaps it's a
>different peice of the same problem.   (Which, as Pat pointed out, is
>one of the heavy prices of moving from a serial syntax to a graph
>syntax.   No debate there.)
>>  2/ RDFO is non-monotonic.  The retrievals from IB2 include information that
>>     cannot be retrieved from IB1.
>>  It is possible to overcome these problems, at least partly, by exploiting
>  > the reflective properties of RDF.  We can encode the disjunctions using a
>>  special construction, something like
>>  IB3	John rdfor:or _:l1 .
>>	_:l1 rdfor:fact _:f1 .
>  >	_:l1 rdfor:rest _:l2 .
>>	_:l2 rdfor:fact _:f2 .
>>	_:l2 rdfor:rest rdfor:nil .
>>	_:f1 rdfor:predicate married .
>>	_:f1 rdfor:object Susan .
>>	_:f2 rdfor:predicate friend .
>  >	_:f2 rdfor:object John .
>Yeah, this works.   It could be seen as going back to a serial syntax,
>of course.

No, it does NOT work. If you publish that as RDF, you are not saying 
what the RDFOR was saying. There is no way to get around this fact, 
since the RDF spec itself includes the RDF MT, so the meaning of that 
RDF is *required by the W3C spec* to be what it is. You might have 
something else in mind; but that is irrelevant, since once those RDF 
triples are set loose on the web, your state of mind or intentions 
are lost; something reading this only has the triples and the RDF 
spec to go on. And with RDF in its current state, there is no way to 
indicate *in RDF* that you mean it to say anything other than what it 
says in RDF.

>  > Now retrieval for RDFOR can (probably) be designed so that
>>  1/ All the extra consequences involve special the RDFOR constructs, and so
>>     can be regarded as benign. 
>>  2/ RDFOR is monotonic.
>>  Have we succeeded?  Partly, but at three prices, two that show up right
>>  away and one that shows up in other extensions.
>>  The first price is that the construction is much more complicated than
>>  a syntax extension. 
>Alas, yes, but that's just because you're looking at it in N-Triples.
>LISP syntax is rather elegant unless you put all the dotted pairs back
>in, then it's about this ugly.

Not quite, in fact. But look: it *is* Ntriples. There isn't any 
'other way' to look at it (except RDF/XML, ie). This is the level at 
which the meaning is attached. You may have in mind that it is being 
used for some other purpose, but that's not what the published spec. 

>  Any object representation system is
>pretty ugly at the bit level.
>>  The second price is that the construction adds a lot of extra consequences.
>>  These consequences can be considered to be benign, but they are still
>>  there.  To make the formalism work correctly in the presence of these
>>  consequences requires a lot of work (and may not be possible, even here).
>Yes.   It will take some work make sure they stay benign.

I don't see how this can be possible. Who knows what consequences 
they might have in some other context, eg when added to some other 
set of triples from some other source? There certainly could be no 
way to guarantee that they might not, for example, accidentally 
combine to be an encoding of some other higher-level syntax (RDFX or 
RDFY) which could mean something else completely. When lists are 
decomposed into sets of triples, and any set entails all its subsets, 
and subsets can be combined freely, the whole idea of using triple 
stores as datastructure encodings strikes me as highly dubious.

>>  The third price is that we have introduced a form of reification and a
>>  construct that can assert the truth of reification constructs.  This
>>  (probably) doesn't cause any problems here because the extension is so
>>  expressively limited.  However, for more powerful extensions reification
>>  produces paradoxes, and thus cannot be used. 
>Two answers here.
>1.  I've heard some people say, "Who Cares?"  Operationally, what's
>the problem with a paradox?

Oh dear God, I am inclined to give up at this point. Why don't y'all 
try making a semantic web which is freely paradoxical, and we go away 
and make one that preserves meaning, and we just see which of them is 
more use?

>  My guess is it will show up as infinite
>loops and/or bottomless recursion, which is unpleasant but can be
>managed as a resource-management problem.

No. It will show up as two pieces of software accessing the same DB 
but one deciding that you owe the bank $2000 and the other deciding 
that the bank owes you $3000, and they are *both right*. That is, 
they are both conforming to published specs which are supposed to 
guarantee that meaning is preserved, and they both use logically 
secure methods, they both have checked their proofs, and both proofs 
are guaranteed to be correct, and they use the same premises; but 
they disagree. That is what happens when DB reasoning hits paradoxes. 
That could happen right now if one of then uses RDF and the other 
uses DAML+OIL and they follow the letter of the published specs.

The point is that we are not here worrying about whether or not the 
software terminates. This isn't to do with computability; its to do 
with what the actual data *means*.

>  That is, in theory there's
>a huge difference between a paradox and a problem that will simply
>take 4 hours to terminate, but operationally they're both just systems
>that go off into the weeds.  The user presses "stop" and everything's
>fine again.

There is so much wrong with this that Im at a loss to cover it all. 
First, please stop talking in kiddie metaphors ("weeds" can mean 
nontermination, bad data, bad reasoning, goodness knows what else). 
Second, paradox doesn't mean nontermination, cf above. Third, there 
is no user to press "stop" on the SW, right? (Isn't that the whole 
point of the SW, as opposed to the WWW? Thats why the 'A' in 'DAML' 
is from 'agent'.) Fourth, the issue is not stopping, but what to do 
with contradictory information that isn't in fact a real 
contradiction but arises from a contradictory specification.

>2.  I don't really like systems going off into the weeds.  And I don't
>see why they have to, if we're careful about the feedback loop.

What feedback loop? (What the hell are you talking about?)

>  That
>is: reasoners should not look for their inputs in their own outputs.

1. Who said anything about this?? 2. Why should they not, in any 
case? If a reasoner uses valid reasoning processes to draw a 
conclusion, then why should it not go on to use that conclusion to 
draw other conclusions? (Ever hear of forward reasoning?)

>Can that loop be avoided if there are two reasoners...?  Hm.  I think
>so, but it might be expensive.
>If you still say that wont work, is there some system I can construct
>(in code or just detailed specification) to demonstrate it will?  Like
>finishing up my FOL-encoded-in-RDF system?  If I can have RDFS and FOL
>reasoners properly attached to the same database, would that be

That would convince me that I was right, since those two reasoners 
couldn't possibly draw the same conclusions from the DB.

Pat Hayes

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Received on Friday, 11 January 2002 19:21:58 UTC