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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: Thu, 20 Feb 2003 12:43:08 -0600
Message-Id: <p05111b1cba7ac785cbac@[]>
To: "Jeff Z. Pan" <pan@cs.man.ac.uk>
Cc: <www-rdf-comments@w3.org>, bwm@hplb.hpl.hp.com

>  > ----- 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: Tuesday, February 18, 2003 12:31 AM
>>  Subject: Re: Comment on Last Call Working Draft of RDF Semantics document
>>  concerning treating classes and properties as objects
>Dear Pat,
>>  Most of the issues raised by this comment have already been addressed
>>  in various archived email discussions, many of them concern other
>>  languages than RDF(S), and many of them are opinions rather than
>>  facts.
>>  I will give a summary of my own personal responses in this message. A
>>  more formal response as Editor may follow later, after consultation
>>  with the WG.  Right now however I do not see in this message any
>>  comments which can be responded to editorially, since they do not
>>  directly impinge on the text of the RDF Semantics document but seem
>>  to be a much more broad-based commentary on the entire RDF enterprise.
>First of all, thank you very much for your interesting comments. I appreciate
>>  >*Problem 1 (Too few entailments) [1]: In "RDF+ MT", closure rules are
>>  >to represent semantic conditions to facilitate entailment.
>>  Strictly speaking that is not quite accurate. The normative model
>>  theory itself does not refer to closure rules: they are described in
>>  informative parts of the RDF semantics document in order to give a
>>  basic syntactic characterization of the valid inferences sanctioned
>>  by the MT, as a convenience for implementers of inference engines.
>I am not quite sure about this. Without closure rules, how does the normative
>  model theory specify that rdfs:subClassOf is transitive?

Er...by saying that it is transitive? But in fact, section 3 says:

<x,y> is in IEXT(I(rdfs:subClassOf)) if and only if x and y are in IC 
and ICEXT(x) is a subset of ICEXT(y)

and the transitivity follows from the transitivity of the subset relation.

>>  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'?

>>  The extra semantic conditions one requires for OWL-RDF are based not
>>  on comprehension from assertions, but on a recursive closure
>>  principle applied to terms,
>But according to section 5.2 of [7], the extra semantic conditions rely on the
>comprehension axioms (conditions). Or maybe we are not talking about the
>same thing?

I am not responsible for the wording used in [7], but I stand by my 
distinction (using the language of set theory).

The term 'comprehension principle' is traditionally used to refer to 
an inference principle which asserts that sets exist corresponding to 
open sentences, of the form 'the set of x such that P' where P is the 
open sentence. In other words, it requires sets to exist which 
satisfy syntactic expressions. Closure conditions, in contrast, 
require that sets exist on the basis of the existence of other sets, 
in the same way that almost all axiomatic set theories are stated. As 
is well known, comprehension principles are dangerous (Russell 
paradox) but these dangers are not inherited by the use of closure 
conditions, which provide the solidest foundations of consistent 
mathematics yet known. That is why we used closure conditions rather 
than comprehension principles in the OWL-RDF semantics.

>  > >*Problem 3 (Size of the Universe)[3,4]:
>>  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. 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, 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'. 
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? :-)

>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. 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".

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 
from Qu Yuzhong which I think makes the same point.

Would it be OK to interpret your comment as an endorsement of #qu-03 ?


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Received on Thursday, 20 February 2003 13:43:14 GMT

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