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Re: LANG: compliance levels

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Thu, 2 May 2002 20:16:54 +0100
Message-ID: <15569.37030.788631.771297@merlin.oaklands.net>
To: Frank van Harmelen <Frank.van.Harmelen@cs.vu.nl>
Cc: Deborah McGuinness <dlm@ksl.stanford.edu>, www-webont-wg@w3.org
On May 2, Frank van Harmelen writes:
> Ian Horrocks wrote:
> 
> > > > when it seems more reasonable/precise to use an
> > > > existential (all countries have a totalArea and it is of type
> > > > xsd;decimal).
> 
> Deb McGuinness replied:
> 
> > > This is not completely correct.
> > > What you are really saying as of course you know well with an existential is
> > > that there is at least one value of totalArea and it is of type decimal.
> > > You have left open the option for another total area to exist which is not a
> > > decimal.
> > > You would have to add that totalArea is functional in order to obtain accurate
> > > conceptual modeling.
> > 
> > I said it seems MORE reasonable/precise. I was arguing that universal
> > -v- existential is not always just a matter of style, and that
> > universal is sometimes used when existential is more appropriate.  
> 
> It is clear that neither universal nor existential do the job on their own here:
> - universal states that all totalArea's must be of type decimal,
>   but does not enforce that there is at least one
> - existential states that there is at least one totalArea of type decimal,
>   but allows for other totalArea's to be of other (silly) types
> 
> This does not support the claim that one is more precise than the other in this case.

You are ignoring the existential quantifier in front of what I said:
"universal is sometimes used when existential is more appropriate";
proof - one example given; QED.                                      (1)

I never said that one is more precise than the other in ALL
cases: I don't believe that and have no doubt that examples of the
opposite kind could be found.

Just to be pedantic though, with the combination of existential and
functional roles does allow one to "do the job" in this case; this is
not true for the combination of universal and functional roles.

> In general: I thought you were out to argue that we cannot find a decent total ordering on many language features. You are now overstating the case for existentials so much that you end up arguing that much/most use of universal is ill-construed, and people mean existential most/all of the time, which sounds like arguing for a total ordering between these two.
> 

I was out to argue this. Here is how it goes:

Theorem: There is no total ordering on language features in all cases.

Proof: Let us assume that such an ordering exists. In (1) I proved
that existentials are better than universals in some cases, so it
can't be the case that universals are better than existentials in all
cases. Therefore, existentials must be better than universals in all
cases. You argue, however, and I am happy to agree, that there exists
at least one case in which universals are better. This is a
contradiction. Therefore our premise must have been false. QED.

> However: 
> all this has become a rather silly discussion after tonight's teleconf.
> Can we not just simply agree that the full language needs both,
> and stop arguing over which one is more useful?

Agreed.

Ian


> 
> Frank.
>    ----
Received on Thursday, 2 May 2002 15:20:27 GMT

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