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Re: Are literals owl:Things?

From: Antoine Zimmermann <antoine.zimmermann@deri.org>
Date: Fri, 15 Oct 2010 12:16:44 +0200
Message-ID: <4CB82A0C.30203@deri.org>
To: Jeremy Carroll <jeremy@topquadrant.com>
CC: Toby Inkster <tai@g5n.co.uk>, Jesse Weaver <weavej3@rpi.edu>, semantic-web@w3.org
Jeremy,


Consider the question:

<< Is "42"^^xsd:integer an xsd:decimal? >>

What would be your answer to this question?  I think it could be:

  1) with a proof-theoretic perspective, it's a syntax error, it's 
impossible to infer:

  "42"^^xsd:integer rdf:type xsd:decimal .

because it's not part of the language;  or it could be:

  2) with a model-theoretic perspective, the answer is definitely Yes! 
because the xsd:integer is a subtype of xsd:decimal.

My bet is that most people would answer this question with a 
model-theoretic perspective.  And my other bet is that the question 
would be asked with that perspective in mind (that is, the asker is not 
asking the truth value of a formula but rather asking a technical 
question about the semantics of RDF(S) or OWL).


Le 14/10/2010 20:08, Jeremy Carroll a écrit :
> On 10/14/2010 9:16 AM, Antoine Zimmermann wrote:
>>
>> Another way of answering the question (which I would coin the
>> "model-theoretic view") is to ask:
>>
>> are the interpretations of a rdfs:Literal included in the
>> interpretations of owl:Thing?
>
> The model theory is not an interoperability point.

Hmm, I don't see what you are trying to say with this.  In what way is 
it related to the initial question?

> They help define the
> interoperability points - entailments etc
> To compare the interpretation of some URI in one model theory with the
> interpretation of the same URI in some other model theory is a category
> error ( ... the beginning of madness ... )

I am not doing this.  I'm comparing different model theories, not the 
interpretations of a URI across model-theories.  To do that, I'm 
describing how the interpretations of 2 distinct URIs are connected, 
within the /same/ model-theory.

In RDF, both rdfs:Literal and owl:Thing are arbitrary URIs so there is 
no connection between them /a priori/.
In RDFS, rdfs:Literal must be interpreted as the set of literal values, 
which contains at least all character strings.  owl:Thing is not a 
particular URI in RDFS, so it can be interpreted arbitrarily, so there 
is no connection between rdfs:Literal and owl:Thing in that semantics.
In OWL DL, rdfs:Literal and owl:Thing must be interpreted as two 
disjoint sets.
In OWL Full, owl:Thing has the same extension as rdfs:Resource, so it 
must contain all literals.


> Questions about RDF or OWL model theory, are, from the point of view of
> the Web user, about as well formed as questions about angels and pinheads.

I'd like to remind you that the very question that started this thread 
is the one asked by Jesse Weaver who, in his email, explicitly mention 
the model-theoretic semantics of OWL.  Thus, the answers are, quite 
appropriately, referring to the model-theory of OWL and RDF.

> ===
>
> The crucial part of
> http://www.w3.org/TR/2009/REC-owl2-direct-semantics-20091027/#Interpretations
>
> is the phrase:
> "disjoint with /Δ_I / "
>
> my assertion is that this phrase is not externally visible - I haven't
> checked that.
>
> I wonder if this was an unnecessary addition. i.e. that all interesting
> theorems about OWL follow even if that part of the defn is omitted.

This is a strict necessity in the DL-based semantics.  Perhaps it would 
be possible to devise a description logic where datatypes and classes 
can overlap but as far as I know, it's been very little studied (maybe 
for some good reason which I don't know).


Regards,
-- 
Antoine Zimmermann
Researcher at:
Laboratoire d'InfoRmatique en Image et Systèmes d'information
Database Group
7 Avenue Jean Capelle
69621 Villeurbanne Cedex
France
Lecturer at:
Institut National des Sciences Appliquées de Lyon
20 Avenue Albert Einstein
69621 Villeurbanne Cedex
France
antoine.zimmermann@insa-lyon.fr
http://zimmer.aprilfoolsreview.com/
Received on Friday, 15 October 2010 10:17:24 UTC

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