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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 09:41:40 -0600
Message-Id: <p05111b46ba7c6c2f8b60@[10.0.100.86]>
To: "Jeff Z. Pan" <pan@cs.man.ac.uk>
Cc: <www-rdf-comments@w3.org>

>  > >[...]
>>  >
>>  >>  In a semantic extension, such as OWL, which does allow this kind of
>>  >>  expressivity, the model theory does indeed need to be further
>>  >>  constrained by imposing appropriate closure conditions. The OWL-RDF
>>  >>  model theory does this, for example. However, *any* such semantic
>>  >>  extension will *always* need to have suitable extra constraints
>>  >>  added, since RDFS itself assigns no meaning to these constructs.
>>  >
>>  >I have to say, well, adding new syntax as well as corresponding semantic
>>  >  constraints is ok. However, adding *missing* objects is quite unusual.
>>
>>  Not sure if I follow you here. There are many constructs in OWL that
>>  are not in RDFS; are those considered 'missing'?
>
>Let me put it this way. Because classes and properties are treated as objects,
>all the objects of the expected classes should be added (i.e. by explicitly
>stating
>that they exist) to the universe before  the extra semantic 
>constraints are added
>for the extended languages.

But in the case we are talking about, the extra semantic constraints 
ARE that the universe is required to contain certain class objects. 
This is not in the least unusual, by the way: this is how the 
classical HOL model theory is built on top of a Tarskian FOL model 
theory, by requiring the relational domains to contain *all* 
relations over the universe of next lower type, and it is also how 
the classical Herbrand universe is constructed, by requiring it to be 
closed under syntactic recursions.

....
>.....
>Very interesting. Thank you. By the way, OWL-RDF semantics [5] calls
>them comprehension conditions,

Hm, maybe I am guilty here, I seem to recall that usage. Whoops.

>maybe you call them closure conditions.
>That's fine. Now my point is that then we've got to make sure we have
>considered all the needed objects exist, favourably by providing a formal
>proof.

Right, and we did, right? Peter did, in fact.

>
>>
>>  >  > >*Problem 3 (Size of the Universe):
>>  >[...]
>>  >>  This is formally correct, and has been noted before, also in archived
>>  >>  Webont email discussions, but I do not consider it to be a 'problem'.
>>  >
>>  >If this is formally correct, then OWL-RDF MT formally might have such
>>  >a problem.
>>
>>  Or might not. Please point to the problem.
>
>As pointed out in problem 3 of [6], such an interpretation is possible in FOL,
>but
>not in OWL Full.

[6] does not give enough detail for me to identify the problem.

>
>
>>I am confident that there
>>  is no mathematical problem, and unless you can find any error in
>>  Peter's proofs in the OWL semantics document,
>
>In my impression, OWL tries to avoid some expressive power from
>  RDFS by considering only ontologies in abstract syntax in the theorems [5].

That is referring to OWL-DL. The 'comprehension' principles are 
required for OWL-Full.

>Therefore, I think Peter's proof won't guarantee that there is no problem
>  with OWL-RDF MT.

I think it does.

>
>>  I see no reason to
>>  think there might be. And in any case this issue should be addressed
>>  to Webont.
>>
>>  >  > The RDFS language allows existential quantification over properties
>>  >>  and classes. This is part of the original design of the language, not
>>  >>  something imposed on it by the semantics. Given this essentially
>>  >>  syntactic property of the language, given the existence of deployed
>>  >>  code which can handle this situation, and given our WG charter to
>>  >>  clarify rather than change the formalism, it would have been
>>  >>  irresponsible, in my view, to have insisted on imposing a textbook
>>  >>  model theory [...]
>>  >
>>  >I totally agree with you here. But on the other hand, it is also unfair to
>>  >  force the upper layer FOL languages have unfamiliar atmosphere in
>>  >  their semantics just because of the WG charter.
>>
>>  I do not think I can respond to the term 'unfamiliar atmosphere'.
>
>I stole a similar phrase from what a CL expert said - "I agree that
>things happen in CL that have an air of unfamiliarity." - in the following
>discussion:
>
>http://philebus.tamu.edu/pipermail/kif/2002-September/001268.html
>
>In other words, CL has some features that other FOL languages
>don't have.

Touche; but you know, this is a VERY trifling point, seems to me. 
Many FO languages have features that are unfamiliar if one is used to 
a slightly different syntax. The only difference being talked of here 
is that classical FO quantifiers range over a subset of the CL 
universe, which is a very familiar and simple kind of transformation, 
arising when comparing eg typed versus untyped logics. So simple 
quantification in FOL syntax needs to be treated as a restricted 
quantification in CL syntax. In every 'logical' way - model theory, 
proof rules, metalogical properties - CL and RDFS are fully 
first-order.

>So it is desirable to have both styles being able to be
>built on top of RDFS.

Well, true, but I think that both styles can be built on top of RDFS 
if one takes care to do it properly.

>  > Personally I have been breathing this kind of air for many years and
>>  find it highly congenial. It has been used by working KIF code which
>>  has been available for over a decade. It is used by CYC and by
>>  OntologyWorks. The CL draft ISO standard is going to be constructed
>>  this way. Why should I not respond that it is your responsibility to
>>  get used to the air at this height? :-)
>
>I am already getting used of it :)
>
>
>>  >Therefore, it would
>>  >  also be desirable to have a subset of RDFS (e.g. RDFS(FA)) such
>>  >  that when FOL languages are built on top of it, they
>>  >have their traditional semantics,
>>
>>  If you build them properly, this is true already.
>
>I am afraid I don't quite follow you at this point.

See above. If you take care which universes your quantifiers range 
over (which is a good idea, in general) then FOL languages do have 
their traditional semantics when built on top of RDFS (or CL, more 
generally). The syntactic mapping used in the 'building' needs to be 
slightly different from the one you may be used to, but the 
difference is small and the change to the mapping is needed in any 
case in realistic situations (where one has to allow for the 
possiblity of different ontologies having different domains of 
discourse).

>
>>  But read on....
>>
>>  >and highly optimised implementations of
>>  >FOL (or its decidable subsets) can be employed. This is what I meant
>>  >by "an alternative approach".

Just to clarify, there is nothing in the current approach which 
prevents highly optimised subsets of the language being identified 
and suitable implementations being employed.  I anticipate that the 
evolution of such subsets will be a major factor in the deployment of 
the SWeb; one sees it happening already in the various optimised 
subcases for OWL.

>  >
>>  Since several comments have made a similar suggestion, and in view of
>>  the need to give a clean account of the relationship between the
>>  various OWL sub-languages and RDFS, I am sympathetic to the idea of
>>  defining what might be called a layered subset of RDFS, intended to
>>  be forward-compatible with OWL-DL in a way that parallels the
>>  relationship between 'full' RDFS and OWL-Full.
>>
>>  There is a logged comment
>>  http://www.w3.org/2001/sw/RDFCore/20030123-issues/#qu-03
>>  from Qu Yuzhong which I think makes the same point.
>>
>>  Would it be OK to interpret your comment as an endorsement of #qu-03 ?
>
>They are similar, although RDFS(FA) is not only an "ontology
>  language", but also a "meta-language" (in Qu's term).

Yes, I understand. With that caveat, could we treat your comment as 
an endorsement of Qu's? This is a procedural question rather than a 
substantive one, you understand.

Pat
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Received on Monday, 24 February 2003 10:41:33 GMT

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