Re: RM formalism supporting partial information

On 29 nov, 03:54, David BL <davi..._at_iinet.net.au> wrote:
> On Nov 29, 12:15 am, Jan Hidders <hidd..._at_gmail.com> wrote:
>
>
>
> > On 28 nov, 01:58, David BL <davi..._at_iinet.net.au> wrote:
>
> > > On Nov 27, 9:43 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
>
> > > > On 26 nov, 15:06, David BL <davi..._at_iinet.net.au> wrote:
> > > > > On Nov 26, 7:47 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
> > > > > > On 26 nov, 08:52, David BL <davi..._at_iinet.net.au> wrote:
>
> > > > > > > Firstly a minor nit pick: you can't say "possible answers", because
> > > > > > > they don't actually represent an upper bound on the result in the
> > > > > > > omniscient database.
>
> > > > > > ?? They do so by definition.
>
> > > > > What I meant was that unless CWA is available on an appropriate
> > > > > projection there may be so much missing information (eg all
> > > > > information about an entity) that the query purported to return the
> > > > > "possible answers" does no such thing. ie it suffers a similar
> > > > > problem to negation (it returns neither the certain nor the possible
> > > > > answers).
>
> > > > I'm not sure what you mean by "the query purported to return the
> > > > 'possible answers'". If the user formulates a query then this will now
> > > > include an indication of whether he or she wants the possible/certain
> > > > answers. It is up to the DBMS to efficiently compute the answer, and
> > > > this is not necessarily done by the usual translation of calculus to
> > > > algebra or even one very similar to it.
>
> > > Consider a query to find all the 27 year old pilots from a census
> > > recorded in an RDB. If the age or occupation is missing we could
> > > think of the person as a possible answer. However we cannot say the
> > > query returns all possible answers unless we assume every person took
> > > part in the census.
>
> > Ok. Forget my other reply, for some reason I had missed something very
> > simple. Whether the suggested computation gives you all possible
> > answers or not depends on the query that is being asked. If it
> > concerned only the persons that took part in the census and you are
> > assuming the CWA for the value-unknown interpretation, then it does.
> > If you really meant all persons, then it doesn't, and you need another
> > computation if you want that answer.
>
> The concept of "possible answers" isn't universally applicable, and
> therefore seems to represent quite a problem for any model of partial
> information that emphasises that concept as fundamental.

The concept of 'possible answers' applies and is well defined for all databases where you have precisely defined what it means if certain data is missing, and note that his includes the definition that says that it means nothing. So what you mean by "isn't universally applicable" is completely beyond my comprehension.

> Did you read my response to Brian regarding the approach to absorb the
> CWA/OWA distinction into the intensional definitions?

Yes, I did. Typical case of "let's redefine our terminology to make the problem go away". :-) It won't do.

> What do you think of the suggestion that the formalism (which is
> concerned with extensions rather than intensions)
>
> 1) ignores the CWA/OWA distinction;
>
> 2) assumes the CWA applies everywhere; and
>
> 3) null is *always* interpreted as non-existence w.r.t.
> the (carefully worded) intensional definitions?
>
> This approach seems simple and self consistent.

If I ignore for the moment 1) (because 1) and 2) seem contradictory because I cannot assume there is no difference between X and Y and at the same time assume that only Y applies everywhere) this is just the classical value-does-not-apply interpretation.

> It doesn't however, attempt to model the case of "value exists but is
> unknown". IMO that case should be modeled *explicitly* with a
> different predicate.Of

Sure, the value-does-not-apply interpretation can always also be represented without null values.

The thing is that you have now fully ignored the real problem of incomplete information which is that in practice the CWA does not always fully apply. Your main solution seems to be to redefine the meaning of the relations such that it does, which, of course, doesn't solve anything at all and simply puts the problem back on the plate of the user.

• Jan Hidders