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Re: A Model Theoretic Semantics for DAML-ONT (now, an Axiomatic Semantics)

From: Je'ro^me Euzenat <Jerome.Euzenat@inrialpes.fr>
Date: Fri, 1 Dec 2000 09:20:07 +0100
Message-Id: <a05010402b64c689e641c@[194.199.17.136]>
To: pat hayes <phayes@ai.uwf.edu>, Dan Connolly <connolly@w3.org>
Cc: www-rdf-logic@w3.org
Hi all,

In his message (Re: A Model Theoretic Semantics for DAML-ONT  (now, 
an ) of 29/11/00,
pat hayes wrote:
>>Guha wrote:
>>>
>>>  Ora,
>>>
>>>   I think they *are* supposed to be disjoint.
>>
>>That's good, since you can deduce that they're disjoint
>>from this semantics
>>
>>DAML-ONT Axioms
>>http://www.ksl.stanford.edu/people/dlm/DAML-Ont-kif-axioms-001127.html
>>Tue, 28 Nov 2000 05:16:36 GMT
>>
>>er... at least I think you can... where did the
>>axioms about what a class is (set of singletons)
>>and what a property is (a set of pairs) go?
>>They were in an earlier draft, no?
>>
>>Anyway, the proof goes:
>>
>>	Every class is a set of singletons
>>	Every property is a set of pairs
>>	nothing is both a singleton and a pair
>>	=> the intersection of classes and properties is empty.
>
>That would be valid, certainly, but why is a class a set of 
>singletons? (Shouldn't a class be allowed to be a set of anything? 
>What is the utility of restricting it to singletons? For example, 
>couldnt I have a class of, say, people, rather than singletons of 
>people?)

Yes I am affraid that it was set of individuals. No? (by indivual I 
mean element of the domain of interpretation).

I would add that, strictly speaking, these sets (the interpretations 
of classes and properties) are not necessarily disjoints. If the 
pairs can be considered part of the domain of interpretation, then, a 
property is interpreted as a class (and we can have class C = 
property P).
To my opinion this is not a very important issue as long as we do not 
start to have the classes and properties as individual.

With regard to that matter, I am also a bit confused by the very 
simple image of RDF(S) provided here (which seems to be very simple: 
labeled
directed graphs) and the example that we can see from time to time 
(e.g. the domain of a relation is a "resource" and a relation itself 
is a resource, from this you can immediately conclude that the set of 
pairs can be in (the interprertation of) the domain of a relation and 
these pairs are not anymore restricted simple pairs of individuals). 
This and everything that can be done with reification is more than 
the simple labeled directed graphs (because, reification add 
constraints on the valid graphs which are not neglectible).
I am not a specialist of RDF so I might be totally wrong about that 
and maybe the whole RDF is relly about labeled directed graphs (and 
maybe all the models are homomorphic to a model expressed as a 
labelled graph these can be taken as a kind of herbrand universe, but 
we are still far away from that). But this is really puzzling of RDF 
(and RDF(S)).

This should be part of the discussion about the domain of interpretation.
-- 
  Jérôme Euzenat                  __
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Received on Friday, 1 December 2000 03:21:43 GMT

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