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Re: DAML-ONT: the case for closedness

From: Je'ro^me Euzenat <Jerome.Euzenat@inrialpes.fr>
Date: Thu, 19 Oct 2000 17:41:28 +0200
Message-Id: <p04310100b614c40729bb@[194.199.22.158]>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, Frank.van.Harmelen@cs.vu.nl
Cc: www-rdf-logic@w3.org
Hello,

In his message (Re: DAML-ONT: the case for closedness) of 19/10/00,
Peter F. Patel-Schneider wrote:
>From: Frank van Harmelen <Frank.van.Harmelen@cs.vu.nl>
>Subject: Re: DAML-ONT: the case for closedness
>Date: Thu, 19 Oct 2000 14:57:20 +0200
>
>>  Je'ro^me Euzenat wrote:
>>
>>  > [FvH: He wants to express the distinction between:]
>>  >
>>  > - "a car is a vehicle with four wheels" and nothing else can be said
>>  > about cars (but if course you can have refinement of the car concept,
>>  > but these are not all the cars)
>>  > and
>>  > - "a car is a vehicle with four wheels" and you can add many more
>>  > assertions about cars in general which will restrict the meaning of
>>  > that concept that I do not know to characterize more precisely and
>>  > that you can refine depending on your needs.
>>
>>  This is exaclty what is known as "defined classes": classes for 
>>which necessary and sufficient conditions are given, and for which 
>>it is stated that these conditions are indeed necessary and 
>>sufficient for this class.
>
>Jerome may want something a bit different, namely a primitive class (i.e.,
>a class that has only necessary conditions for membership) that cannot be
>further refined.  I'm not sure what good this is, except perhaps in the
>philosophy of religion (unknowable mysteries whose limits of knowledge have
>been reached, etc., etc.).  If some other modeller wants to augment the
>properties of a primitive class then I don't see why this should not be
>allowed.  Of course this other modeller can get into trouble by adding
>properties that should not be there, but I don't see that the goal of a
>modelling language is to prevent modellers from doing wrong things, nor
>do I see that there is any way of preventing such mistakes in any case,
>even if that was desired.

This is even more different, because, in my understanding, this also 
applies to defined concepts.

In the scheme taken in OIL (or at least in FaCT), and similarly in 
DAML-ONT, the definitions are given by axioms. It is legitimate to 
have several defining axioms for the same concept. E.g.

equilateral-triangle = (all-equals angles.measure)
equilateral-triangle = (all-equals edges.length)
[assuming a all-equals is a constructor interpreted as all the values 
in relation must be equal]

This is perfectly correct because E((all-equals 
angles.measure))=E((all-equals edges.length))
[E(.) being the extension of a term]

But you can also, as Peter gave it as an example, write:
Nothing=Everything
(this is a second definition for both terms: A and not A, A or not A).

Would it not be nice to be able to say: what I mean by "Everything" 
is exactly the the interpretation of "A or not A" and thus you must 
not add new definitional axioms for "Everything"?

Hope this clarifies,
-- 
  Jérôme Euzenat                  __
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Received on Thursday, 19 October 2000 11:42:50 GMT

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