Re: RM formalism supporting partial information

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:
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> > On Nov 24, 3:56 am, Jan Hidders <hidd..._at_gmail.com> wrote:
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> > > On 21 nov, 04:05, David BL <davi..._at_iinet.net.au> wrote:
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> > > > By consistency I only mean the inability to derive self contradictions
> > > > that would make it impossible for the definitions to be satisfied in
> > > > the first place. Of course it is normally impossible to prove
> > > > consistency. I think this is quite different to your usage of
> > > > "consistency" in the above. Is that right?
>
> > > Yes. I meant that you are not consistently using or defining a single
> > > interpretation of missing data but rather seem to taking sometimes one
> > > and sometimes the other depending on what make the math looks cute.
> > > That approach is likely to end in elegant but meaningless results.
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> > AFAIK you say this because of something to do with the CWA but I can't
> > get past the feeling that the CWA is incompatible with partial
> > information and that's all there is to it! Perhaps you could give me
> > an example to back up that statement.
>
> For the classical CWA you are right, but it comes in many sizes and
> shapes these days. The Reiter paper I mentioned basically is about
> which how to adapt the CWA for a certain interpretation of null
> values. That would be the first example I would point you to.
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> > I have wondered whether what you're after is a model that allows the
> > CWA to apply to some projections and not to others.
>
> Not only projections, also selections, or actually any part of the
> database that can be identified by a query.

So would you say that CWA most generally applies to particular views and not necessarily base relvars?

> > Well I agree, but
> > I still think it's interesting to investigate the simpler case of
> > where the CWA is never applicable.
>
> Really? That case looks rather simple to me. If we consider the usual
> 6 algebra operators from the named perspective then, under the
> assumption that the operations contain the set of certain answers then
> all except the difference also return the certain answers, and the
> difference returns something that is neither the certain nor the
> possible answers.

It is rather simple, but I think that's a good thing! I have doubts whether an intricate model will be worthwhile. I'm put off by the way (in 3vls) unknowns propagate all other the place, so there seems little gain modelling all that, compared to merely propagating what's certain. There seems a lot of complexity and not much to show for all the trouble.

I would say that even this simple case leads into some complexity for anyone interested in practical issues such as query optimisation and physical implementation. For example, in the word document I hadn't yet determined whether my join operator was associative and it would appear that a proof will probably be quite long and arduous. Nevertheless, join associativity is very important for query optimisation. I conjecture a very curious connection between information preservation and associativity. My initial attempts at a join operator were clearly not associative and the trick seems to be to ensure it maintains all information compatible with a logical conjunction with shared variables.

I was wondering as well how these operators may be relevant to the TRM.
> > I might agree with your sentiment more generally for deductive
> > databases, but for the restrictive logical inference used in RM,
> > thinking of negation as failure to prove true seems simple and
> > intuitive.
>
> I have you no idea what you mean with "restricted inference in RM".
> The RM does not prescribe what inference you can or cannot use, so you
> can use full first order logic inference or even more. And if you call
> the CWA one more time "negation as failure to prove true" it might
> decide to sue you for slander. :-)
>
> > > Exactly, so in that sense it is actually complete, and you can make
> > > that claim precise. The set of tupels in the answer will be exactly
> > > the set of tuples that are certain to be in the result of the same
> > > query over the omniscient database. By the nature of the problem every
> > > query should actually return 2 sets of tuples: the set of certain
> > > answers, and the set of possible answers. Your operators should
> > > therefore not operator on relations but on pairs of relations.
>
> > 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). Received on Mon Nov 26 2007 - 15:06:05 CET