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Re: Issue #pan-01 Re: Comment on Last Call Working Draft of RDF Semantics document concerning treating classes and properties as objects

From: pat hayes <phayes@ai.uwf.edu>
Date: Mon, 24 Feb 2003 11:24:49 -0600
Message-Id: <p05111b4bba7ffc85e058@[10.0.100.86]>
To: "Jeff Z. Pan" <pan@cs.man.ac.uk>
Cc: <www-rdf-comments@w3.org>

>  > ----- Original Message -----
>>  From: "pat hayes" <phayes@ai.uwf.edu>
>>  To: "Jeff Z. Pan" <pan@cs.man.ac.uk>
>>  Cc: <www-rdf-comments@w3.org>
>>  Sent: Thursday, February 20, 2003 7:24 PM
>>  Subject: Re: Issue #pan-01 Re: Comment on Last Call Working Draft of RDF
>>  Semantics document concerning treating classes and properties as objects
>>
>>
>>  >----- Original Message -----
>>  >From: "Brian McBride" <bwm@hplb.hpl.hp.com>
>>  >To: "Jeff Z Pan" <pan@cs.man.ac.uk>; <www-rdf-comments@w3.org>
>>  >Sent: Tuesday, February 18, 2003 11:35 AM
>>  >Subject: Issue #pan-01 Re: Comment on Last Call Working Draft of 
>>RDF Semantics
>>  >document concerning treating classes and properties as objects
>>  >
>>  >
>>  >>  Jeff,
>>  >>
>>  >>  With Pat responding that your comments are not editorial, I'm 
>>going to try
>>  >>  to identify the comments you are making for consideration by the WG.
>>  >>
>>  >>
>http://lists.w3.org/Archives/Public/www-rdf-comments/2003JanMar/0283.html
>>  >>
>>  >>  At 21:15 14/02/2003 -0800, Jeff Z Pan wrote:
>>  >>
>>  >>
>>  >>  >Recent research (http://dl-web.man.ac.uk/rdfsfa/paper.htm) 
>>has shown that
>>  >>  >RDF Schema (RDFS) has a non-standard metamodeling architecture, which
>makes
>>  >>  >some elements in the model have dual roles in the RDFS 
>>specification.  As
>a
>>  >>  >result, this can be confusing and difficult to understand and,  more
>>  >>  >importantly, the specification of its semantics requires a non-standard
>>  >>  >model theory - RDF MT. RDF MT justifies dual roles by "treating classes
>and
>>  >>  >properties as objects", which seems to be ok within RDFS. However, this
>>  >>  >leads to semantic problems when we extend RDFS with more expressive FOL
>>  >>  >constructs, and extend RDF MT to the so called ``RDF+ MT'' to 
>>give meaning
>>  >>  >to this extended language:
>>  >>
>>  >
>>  >Brian,
>>  >
>>  >>  Ok - I think you are saying you are trying to extend RDF(S) to some
>>  >>  (proper?) subset of FOL and are having problems.  Yes?  The rest of this
>>  >>  message is an explanation of the difficulties you are experiencing.
>>  >
>>  >It also suggests that it might be a good idea to also locate a 
>>sub-language of
>>  >RDFS
>>  >(e.g. RDFS(FA)) such that when FOL languages are built on it, they can have
>>  >their traditional semantics, and the existing highly optimised
>>  >implementations of
>>  >FOL (or its decidable subsets) can be employed.
>>
>>  It would be very helpful if you could be more precise. My
>>  understanding is that RDFS already has this character,
>
>I hope so, but currently I am not sure (see below).

It all turns on what is meant by 'built on it'.  See end of this message.

>
>>if one
>>  interprets the phrases 'built on' and 'can be deployed'
>>  appropriately, and that the existence of OWL illustrates this.
>>
>>  Your comment can be interpreted, therefore, in several ways.
>>
>>  (1) You do not agree with this understanding - in which case, it
>>  would be helpful if you could document the problems in some detail,
>>  or give examples. (All the issues you mentioned in your first comment
>>  have been dealt with already by the Webont WG, as noted previously.)
>
>Well, I am afraid I don't. In my opinion, "treating classes and properties
>as objects"  brings some unclearness when people layer FOL on top of RDFS.

Can you please say what the problems actually are? The only actual 
problems mentioned in the papers you cite have been adequately 
addressed by subsequent work, notably by the Webont WG, in my view. 
Several of the papers you cite repeat the complaint, but provide no 
actual evidence for it.

If we were to indulge in debate, I would point out that all classical 
formalizations of set theory are essentially first-order (plus some 
axiom schemata in some cases) but obviously treat classes as objects, 
and that the widely used syntactic trick of using a 'holds' predicate 
to embed 'higher-order' assertions in a conventional FOL syntax also 
presupposes that FO universes can contain relations. I would ask you 
to cite any published work in mathematical logic which suggests that 
classical first-order universes of discourse cannot contain entities 
such as classes, properties or relations.

>Three problems were discussed in earlier papers [1,2,3,4] and also in Webont
>WG (see below):
>
>- Problem 1 indicates that we should prove that all the expected (classes and
>properties)
>objects are explicitly required in the universe.

Please clarify. Who is 'we', and what does 'expected' mean?

>
>- Problem 2 indicates that we should also prove that all the 
>contradiction class
>objects
>won't bring any semantic problems for the extended language (e.g. OWL Full).

What kind of proof would you find acceptable? You seem to be asking 
for a consistency proof. Usually, the construction of a nontrivial 
model theory is taken itself to be such a proof, unless you are 
worried about issues in the foundations of mathematics applied to the 
metatheory of the model theory statement itself.

>
>- Problem 3 indicates that we should also prove that the individual objects,
>class objects
>and property objects are handled well enough such that no more 
>semantic problems
>(like
>the "size of Universe" problem) for the extended language.

The phrase 'no more semantic problems' does not seem likely to admit 
of precise analysis, particularly since Goedel. So far I have not 
seen any actual semantic problems, and the overall semantic framework 
that you dislike has been widely applied in several areas of applied 
philosophical logic. While not directly relevant to the semantic web, 
these applications, and the professional competence of the logicians 
who have used the framework, do suggest that there are no deep 
disasters waiting to be discovered. Chris Menzel and  myself have 
published a full model theory for a vastly more expressive logic even 
than KIF or current CL (it allows completely unrestricted application 
of symbols to arguments and unrestricted use of sequence 
quantifiers.) Several months of the Webont WG's time was wasted as a 
result of members protesting about these 'problems', which turned out 
to be imaginary. So unless you can cite actual problems, rather than 
a generalized feeling of unease or concern, then I am not inclined to 
respond in much more detail.

>However, in RDFS an
>individual object can easily and possibly become a class object 
>and/or a property
>object,

In RDFS the implied distinction between layers is not imposed on the 
language itself. If you wish, however, you can impose it, and use a 
'layered' vocabulary in a consistent way, as in RDFS(FA). If you do 
so, nothing will 'become' anything it should not be.

>which makes things really complicated.

On the contrary, it makes things much simpler.

(Clearly, there is no point in continuing such a 'debate'. Please 
document what things are more complicated , and in what way.)

>Without these proofs, I don't believe all these problems have been solved by
>Webont WG
>in OWL Full.

Without some counter-evidence, or some reasons why I should take your 
disbelief seriously, I cannot respond.

>On the contrary, OWL tries to avoid some expressive power from
>  RDFS by considering only ontologies in abstract syntax in the 
>theorems [5], i.e.
>significantly
>restricting the possible form of ontologies. Therefore their proofs 
>by no means
>cover all the
>above three problems.

Please read all the OWL documentation. OWL-Full allows unrestricted 
use of RDFS syntactic freedom, has a well-defined model theory and is 
a semantic extension of RDFS. The result proven by Peter shows that 
if one treats OWL-DL as a syntactic restriction imposed on OWL-Full, 
then theorem-hood is preserved relative to the 'abstract' OWL-DL 
model theory on this subset of the language. Taken together, these 
results are, in my view, a fully adequate formal response to your 
concerns and an adequate response to your demand for proofs of 
consistency.

>So my view is that the FOLs with free syntax [6], e.g. SKIF, can be 
>built on top
>of RDFS, while
>the FOLs without such features can be built on top of a sub-language of RDFS,
>such as RDFS(FA),
>without any unclearness.

You need to clarify what you mean here by 'built on top of'. I 
suspect that you mean it in the sense in which the 'upper' part 
contains *all* of the 'underneath' part as a sublanguage. In this 
sense you are right, of course, since the 'upper' part you refer to 
as 'FOLs without such features' indeed lack some syntactic freedom. 
But this seems to me like someone complaining that he wants to build 
a small building and the foundation is too large; and the obvious 
reply is, then only use the part of the foundation that you need. If 
it were the other way around then you would have a more legitimate 
reason to protest; which is why we cannot insist that the foundation 
be shrunk to more exactly fit your building style, since then others 
would be really shafted.

To advocate restricting ourselves to a foundation on which only one 
kind of building can be erected seems inappropriate, particularly 
when we have made such useful recent progress towards designing a 
truly modular foundation which can be used for a number of different 
purposes. You don't have to use all the foundation if you only want 
to use part of it.

Best wishes

Pat

>
>Best regards,
>Jeff
>--
>Jeff Z. Pan  ( http://DL-Web.man.ac.uk/ )
>Computer Science Dept., The University of Manchester
>
>
>[1] http://www-db.research.bell-labs.com/user/pfps/papers/dl-2002.ps
>[2] http://www-db.research.bell-labs.com/user/pfps/papers/layering.ps
>[3]http://www.cs.man.ac.uk/~horrocks/Publications/download/2003/HorrocksPatelSchn
>eider.pdf
>[4]http://www.cs.man.ac.uk/~panz/Zhilin/download/Paper/Pan-Horrocks-rdfsfa-2002.p
>df
>[5] http://www-db.research.bell-labs.com/user/pfps/owl/semantics/
>[6] http://reliant.teknowledge.com/IJCAI01/HayesMenzel-SKIF-IJCAI2001.pdf
>
>
>>
>>  (2) You feel that the way that OWL was 'built on' RDFS is unsuitable
>>  or inappropriate in some way - in which case, it would help if you
>>  could sketch how you feel it would have been done better on a
>>  sublanguage, ie what you mean by 'built on' which is different from
>>  the relationship between OWL and RDF;
>>
>>  (3) What sense of 'can be deployed' makes OWL-DL not an illustration
>>  of how this is already  possible?
>>
>>  It would also help if you could say more exactly what you mean by a
>>  "FOL language". In my understanding, Lbase, CL and KIF are all FOL
>>  languages, but I take it that this does not satisfy you.
>>
>>  Pat
>>  --
>>  ---------------------------------------------------------------------
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>>
>>
>>


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Received on Monday, 24 February 2003 12:24:43 GMT

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