Re: Interpretation of Relations

Bob Badour wrote:
> Joe Thurbon wrote:
>
> > On 2007-01-20 11:49:20 +1000, "JOG" <jog_at_cs.nott.ac.uk> said:
> >
> >> Joe Thurbon wrote:
> >>
> >>>
> >>>
> >>> NOT Joes hair is Red
> >>> NOT Joes hair is Blond
> >>>
> >>> Is this right?
> >>
> >>
> >> I see nothing wrong with your logic. What you are saying via an empty
> >> relation is that there is no proposition for which Joe has a hair
> >> colour. In fact I think from it you can infer: Joe has no hair colour.
> >
> >
> >> (which given my external knowledge --> Joe has no hair).
> >
> >
> > Not a bad guess, actaully.
> >
> >>
> >>> If so, it leads me to a question about modelling missing
> >>> information. (And a lot of other questions, too). If not, is there a
> >>> simple thing that I've missed?
> >>
> >>
> >> My current understanding is that:
> >>
> >> * If an attribute is Inapplicable then simply stating no proposition
> >> containing it is sufficient for that fact to be inferred.
> >> * If the attribute is Applicable but we do not have value for it, then
> >> we must state this propositionally to avoid inferring it as
> >> inapplicable under the CWA.
> >> * Alternatively if the attribute is 'possible' (we don't know if it is
> >> missing or inapplicable) then we must also state a proposition
> >> reflecting this in order to avoid the inapplicability inference.
> >
> >
> > I'm not sure I follow.
> >
> > When you say "an attribute is inapplicable" I'm guessing that what
> > you're saying is "The domain of my relation is expressive enough to
> > assert a relevant proposition, but, actually, that proposition is false
> > for all elements of that domain?" That seems to be another way of saying
> > "This relation is a reasonable one to invoke the CWA over." Is that what
> > you intend?
>
> I believe JOG refers to a topic introduced to the mainstream by Codd's
> RM V2 (as far as I know), wherein he discussed that NULL is frequently
> used to mean things other than "Unknown" or "Missing". He proposed a
> second kind of NULL for "Inapplicable" where for instance the salary of
> a commission-only salesman is "Inapplicable". In that case, the
> "Inapplicable" version of NULL is treated as 0 for summation. But that
> raises the question of how to calculate average salary. If we have 1
> salesman and 1 salaried employee, is the average salary half of the
> salaried employee's salary?
>
>
> > Actually, I'm not really confident I understand what you mean by
> > applicable and innapplicable.
> >
> > In the second point above, are you saying that, in the Hair Colour
> > example, we'd need a second relation which is basically "Those for whom
> > we know the hair colour" and if Joe doesn't appear in that relation,
> > then we should not make any inferences with respect to the Hair Colour
> > relation. If so, I find this a little problematic: I would have thought
> > that relations should be interpreble when considered individually.
>
> I suspect he refers to the three relations involved in Hugh Darwen's
> paper on replacing NULL with relations. If I am not mistaken, the paper
> is called _The final NULL in the Coffin_ (but if I am wrong and you have
> to read more than one of Darwen's papers, you will receive no harm.)
>
>
> >> It is worth noting that many view db-query results as coming with the
> >> caveat "as far as I, poor naive database, know". Jim.
> >
> > This last comment has helped me flesh out an idea, so thanks. I'm
> > currently trying to work out a (relatively formal) logical
> > interpretation of relations. I'm happy to embellish if you are
> > interested, but I won't foist it on you if you're not. (I hope you are
> > interested, it won't take much to get me started....).
> >
> > Informally, it boils down to: if a database should be considered as a
> > set of logical assertions, then you have to be very careful how you
> > treat missing information, especially in the presence of the CWA. In
> > facts the particular logic in which the facts are being asserted in is a
> > modal logic.
> >
> > In particular, there are two types of relations,
> > - those which should be interpreted as 'facts about the world', which
> > can't really handle missing information, because of the CWA, and
> > - those which should be interpreted as 'facts about my knowledge of the
> > world' which can handle missing information.
> >
> > I must confess, though, that I've not really read widely enough to know
> > if this is a new take on RA. But perhaps someone here can let me know.
>
> Given the lack of any formal theory for handling missing information,
> one would be very welcome. However, any such theory would be quite
> revolutionary--especially if comprehensive. In other words, I won't hold
> my breath and I suggest you not get too disappointed if you try but fail.
>
> If this is a topic you are interested in, I suggest you read _Reasoning
> About Knowledge_ Fagin, Halpern, Moses, and Vardi
> http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=8240
>
> The Fagin in question is the same Fagin who brought us 5NF among many
> other things (although, I don't think the Moses is the same Moses who
> brought us the 10 C's) so the book represents some good serious thinking
> by people who are really adept at it.

Thank you for explicating these points bob. I was planning to do so when I had some crucial work to complete and needed some excuse to avoid doing it, and that hadn't cropped up yet today.

Darwen's paper on null avoidance can be found at: http://web.onetel.com/~hughdarwen/TheThirdManifesto/Missing-info-without-nulls.pdf

"Final Null in the Coffin" was I think by Pascal, and discussed an actual mechanism for a similar approach. However I think given debunk.com's retirement this may now be quite difficult to get hold of. Received on Sat Jan 20 2007 - 16:17:28 CET