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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: Tue, 18 Feb 2003 10:55:00 -0600
Message-Id: <p05111b07ba7812ad35a7@[]>
To: "Qu Yuzhong" <yzqu@seu.edu.cn>
Cc: "Jeff Z Pan" <pan@cs.man.ac.uk>, "rdf-comments" <www-rdf-comments@w3.org>
>I agree with you in that RDFS has a non-standard metamodeling architecture.

I am unable to respond to this comment as I do not know what is meant 
by 'nonstandard'. I am not aware of any 'standard' in this area.

>Although the current RDF Semantics [1] is better than previous 
>version, it still intertwists the ontology language layer and 
>meta-language layer.

I would want these terms to be better defined before giving a 
detailed response to this comment. The overall design of RDF is not 
based on any distinction between 'ontology language layer' and 
'meta-language layer'. I am not aware of any precise meaning for 
these terms.

Most serious ontology work is carried out in languages far more 
expressive than RDFS.

>In other words, RDF Semantics [1] is ambitious in that it tries to 
>give the semantics of RDFS at both of ontology language layer and 
>meta-language layer with a single mechanism.

Indeed it is a unified language with a single semantics. I fail to 
see what problems anyone could have with this; but in any case, this 
overall design was fixed by the original authors and was not imposed 
by the semantics.

If the comment can be paraphrased as the observation that RDFS does 
not support the notion of an ontology/meta language distinction of 
'layers'. then this is correct. It does not.

The language does not strike me as in any sense 'ambitious', being 
little more than a small subset of FOL.

>Two comments:
>1) As an ontology language (at L layer [2]), RDFS should have a 
>clear and fixed semantics based on a subset of FOL (or other well 
>known Logic such as Order-Sorted Logic).

It does have a fixed semantics based on FOL. Whether or not it is 
clear must be a judgement call, but it is defined fairly rigorously.

>The semantics of OWL (as an extension of RDFS at L layer) can be 
>defined by using the same approach.

Similarly, although the primary responsibility for the OWL semantics 
rests on other shoulders.

>2) As a meta-language (at M layer [2]), RDFS should have another 
>semantics (not as the current one).

This is not specific enough to respond to.

I do not accept the distinction between L and M "layers" as being 
particularly meaningful or useful; but in any case, in order to 
respond to this point, I would ask that some concrete reason be given 
to suppose that such a distinction is in some way incompatible with 
the current RDFS semantics.

Pat Hayes

>Yuzhong Qu
>Dept. of Computer Science and Engineering, Southeast University
>Home Page: http://cse.seu.edu.cn/People/yzqu/en
>Research Group: http://xobjects.seu.edu.cn
>[1] RDF Semantics (ed Pat Hayes)  http://www.w3.org/TR/rdf-mt/
>[2] J. Pan, I. Horrocks, Metamodeling architecture of web ontology 
>languages. In Proceedings  of the first Semantic Web Working 
>Symposium (SWWS'01), pages 131-149, 2001. 
>----- Original Message -----
>…l: "Jeff Z Pan" <pan@cs.man.ac.uk>
>l: <www-rdf-comments@w3.org>
>… ”: 2003N215™ 13:15
>’: Comment on Last Call Working Draft of RDF Semantics document 
>concerning treating classes and properties as objects
>>  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:
>  >
>>  *Problem 1 (Too few entailments) [1]: In "RDF+ MT", closure rules are used
>>  to represent semantic conditions to facilitate entailment. However, if the
>>  expected class and/or property  objects are not in the universe, then the
>>  related closure rules are not expressible, which hence leads to too few
>>  entailments. E.g., does "John type (A and B and C)" entail "John type (B
>>  and A)"? No, because the class object "B and A" might not exist in every
>>  interpretation which satisfies " John type (A and B and C)" .
>>  In order to fix the problem, one can/should also introduce, besides the
>>  closure rules, comprehension axioms to add all the possible missing objects
>>  into the universe, e.g. the "B and A" object in the above example. In order
>>  to support FOL constructs in the extended language, a large and complex set
>>  of comprehension axioms (and closure rules) must be added  to capture the
>>  meaning and characteristic of its additional constructs. It is very
>>  difficult to get them right, and it is more difficult to prove that they are
>>  correct (adding enough but not too many objects into the universe).
>>  *Problem 2 (Contradiction classes)[1,2]: Since class and property objects
>>  are distinguished from their extensions, one can then, in the extended
>>  language, define a class eg:C as an instance of itself, and add a
>>  cardinality constraint ``=0'' on the rdf:type property that pointing to
>>  itself. It is impossible for one to determine the membership of this class.
>>  If an object is an instance of this class, then  it isn't, because instances
>>  should have no rdf:type property pointing to itself. But if it isn't then it
>>  is. This is a contradiction class.
>>  According to the comprehension axioms, we must add all possible class
>>  objects into the domain, and the above contradiction class is one of them.
>>  In this way, all the interpretations will have such contradiction classes,
>>  and thus have ill-defined class memberships.
>>  *Problem 3 (Size of the Universe)[3,4]: treating classes and properties as
>>  objects also triggers a problem if we set constraints on the size of the
>>  universe. E.g. is it possible to have an interpretation s.t. Thing <=
>>  {John}, "John type Person", "John type not Car"? It is possible in FOL, but
>>  not in "RDF+ MT". In FOL, the interpretation of John, I(John), is the only
>>  object in the universe; the interpretation of Person, I(Person), is a set
>>  with only one element I(John); the interpretation of Car, I(Car), is an
>>  empty set. In "RDF+ MT", since classes are also objects, John, Person and
>>  Car should all be interpreted as the only one object in the universe.
>>  However,  since I(John) is in ICEXT(I(Person)), but not in ICEXT(I(Car)),
>>  I(Person) and I(Car) should be different. Thus there should be at least two
>>  objects in the universe. In other words, the required interpretation is
>>  impossible in ``RDF+ MT''.
>>  This problem shows that the interpretation of RDF MT has different features
>>  than the interpretation of standard FOL model theoretic semantics. This
>>  raises the question as to whether it is possible to layer FOL languages on
>>  top of both the syntax and semantics of RDFS.
>>  More details about the above three problems can be found in [4].
>>  As a consequence of these problems, when DAML+OIL is layering on top
>>  of RDFS, it uses the syntax of RDFS only, but defines its own semantics [6]
>>   for the ontological primitives of RDFS. Similarly, when the Web Ontology
>>  Language (OWL) is layering on top of RDFS, (slightly but necessarily)
>>  different semantics are defined for OWL DL and OWL Full [7].
>>  Some people believe that Lbase [8] can provide a framework for specifying
>>  the semantics of all of the Web ontology languages in a uniform and coherent
>>  way. However, that might not be so straight forward. To make the model
>>  theory of Lbase as the model theory of all the semantic web languages so
>>  as to make it possible to use a *single* inference mechanism to work on
>>  these
>>  different languages [8], Lbase must at least be expressive enough to allow
>>  direct
>>   mapping from RDF constructs into its constructs. But according to the
>  >  translation rules from RDF graph to Lbase in [9], e.g., rdfs:subClassOf is
>>  not
>>  directly mapped to logical implication in Lbase, but must be explicitly
>>  stated,
>>  or axiomatised as, e.g.rdfs:subClassOf(class1,class2). That is, the
>>   rdfs:subClassOf from RDF and the logical implication from FOL are not
>>  mapped
>>   to the same thing in Lbase, which means there are no (or far less than
>>  enough)
>>   semantic interoperability between RDFS and FOL in the Lbase framework.[3]
>>  So the problem of layering FOL on top of RDFS still exists.
>>  An alternative approach is RDFS(FA) (http://dl-web.man.ac.uk/rdfsfa/) [5,4],
>>  which as a sub-language of RDFS has a relatively standard model theoretic
>>  semantics, such that FOLs, e.g. DAML+OIL and OWL DL, can be built on top of
>>  both the syntax and semantics of RDFS(FA).
>>  --
>>  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/HorrocksPatelSc
>>  hneider.pdf
>>  [4]
>>  http://www.cs.man.ac.uk/~panz/Zhilin/download/Paper/Pan-Horrocks-rdfsfa-2002
>>  .pdf
>>  [5]
>>  http://www.cs.man.ac.uk/~panz/Zhilin/download/Paper/Pan-Horrocks-rdfsfa-2001
>>  .pdf
>>  [6] http://www.daml.org/2001/03/model-theoretic-semantics.html
>>  [7] http://www-db.research.bell-labs.com/user/pfps/owl/semantics/
>>  [8] http://www.w3.org/2002/06/lbase/20030116Snapshot.html
>>  [9] http://www.w3.org/TR/rdf-mt/#Lbase

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Received on Tuesday, 18 February 2003 11:55:04 UTC

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