Re: LANG: compliance levels

Ian Horrocks wrote:

> 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 must not have made my point clearly enough.
While I do not disagree with your statement
"universal is sometimes used when existential is more appropriate"
I disagree with the example you chose to make your point.

Your example is not well chosen to make your case (and in fact it is not well chosen to make either case since it does not need just the existential alone without a statement of functional role and it it does not need just the universal alone without a min cardinality statement).

You said
 (all countries have a totalArea and it is of type xsd;decimal)

I claim that typically when someone says this statement in a natural language, they are not meaning to imply that there can be a total areaFiller of an instance of the class country that is not of type xsd;decimal.
Of course the existential is only restricting ONE of the fillers of totalArea to be of type decimal  thus I claim that the existential alone is NOT a precise model of what you stated in English.

Thus, i disagree that you have a proof by your one example since your example does not make your point.

I do not disagree that there are other examples that make your point that the existential alone can be useful.
I do not want to choose examples where the role is functional since that muddies the water.
An example that does not require functionality to make your point is
KRPaper = a paper that has at least one topic that is an instance of KR.  (this does not say that the paper may not also have another topic that is an instance of something other than KR).

An example of a problem that makes the universal point alone without any need for any kind of cardinality is
Persons have children who are persons.
This is a clean example I state where one needs to have a universal restriction on the hasChild role of the class Person.
If a person has any children, then they are persons.  We should not require a person to have at least one child (which the existential would do) and we should allow them to have multiple children and require ALL of the children to be instances of the class Person.

> 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.

it only does the job in the case where a role is functional.
It is not useful for multi-valued roles.

I do not dispute that functional roles and existentials in combination can be useful, I am just stating that they can not solve ALL of the typical problems that come up in applications.
Similarly I am stating that min cardinality 1 along with universals can be very powerful to express many things that come up in practice, but they will not solve ALL of the representational issues that you or I can point out as useful to represent.

I agree with Frank that it feels to me like you are overstating the case of the power of existentials and I am disputing this overstatement since some people on this mailing list may not be as familiar as you or I with how to model situations.

> > 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.
> >    ----

Agreed - the full language needs both.

--
 Deborah L. McGuinness
 Knowledge Systems Laboratory
 Gates Computer Science Building, 2A Room 241
 Stanford University, Stanford, CA 94305-9020
 email: dlm@ksl.stanford.edu
 URL: http://ksl.stanford.edu/people/dlm/index.html
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Received on Thursday, 2 May 2002 16:30:22 UTC