From: Lynn Andrea Stein (las@ai.mit.edu)
Date: 10/16/00
Ah, one where I can clarify:
Dan Connolly writes:
> In what way is
> The class C is the disjoint union of the classes
> in the list L.
> not an assertion?
[Full context of the quotation below.]
(*) The class C is the disjoint union of the classes
in the list L.
is an assertion.
However, the clause
the disjoint union of the classes in the list L.
is not an assertion and may be meaningless.
I believe that Pat (Hayes) means to be asking what C is asserted (by
(*)) to be in this case.
I believe that Dan's answer would be that the assertion (*) is false.
An alternative answer might be that the assertion (*) is true, but
that "disjoint union" of a non-disjoint class set is ill-defined,
e.g., that (*) is asserting that C is some special "error object".
This is a more operational way to interpret the assertion (*).
Dan and Pat (and everyone else), did I put the right words into your
mouths?
Lynn
Dan Connolly writes:
> [some of these questions/comments are starting
> to make my brain hurt, but some of them are easy.
> Rather than making the easy ones wait for the
> hard answers, I'll answer in parts...]
>
> pat hayes wrote:
> >
> > >pat hayes wrote:
> > > >
> > > > In DAML-ONT:
> > > >
> > > > </Property> <Property ID="disjointUnionOf">
> > > > <label>disjointUnionOf</label>
> > > > <domain resource="#Class"/>
> > > > <range resource="#List"/>
> > > > <comment>
> > > >
> > > > for unionOf(X, Y) read: X is the disjoint union of the classes in
> > > > the list Y: (a) for any c1 and c2 in Y, disjointWith(c1, c2),
> > > > and (b) i.e. if something is in any of the classes in Y, it's
> > > > in X, and vice versa.
> > > >
> > > > cf OIL disjoint-covered
> > > > </comment>
>
> [...]
>
> > > > <! QUESTION: what is the value of your disjoint-union when the
> > >classes arent disjoint?>
> > >
> > >er... the same as the "value" of any other false assertion,
> > >such as 5<4.
> >
> > Nah, but your disjoint-union isn't an assertion, its an operator.
>
> Yes, it is an assertion.
>
> In what way is
> The class C is the disjoint union of the classes
> in the list L.
> not an assertion?
>
>
> > So
> > what its value is when its ill-defined is not so easy to specify.
> > Thats why I jumped on it, in fact: your definition is half assertion
> > (the arguments are disjoint) and half operator/function (like union
> > or intersection), so its neither fish nor fowl. One of the nice
> > things about the classical operations like disjoint-product is that
> > they are pure function, no assertion, so they always have a
> > well-defined value.
> >
> > .....
> [...]
>
>
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