Re: Interpretation of Relations

From: Joe Thurbon <usenet_at_thurbon.com>
Date: Sun, 21 Jan 2007 09:07:01 GMT
Message-ID: <200701211906458930-usenet@thurboncom>

On 2007-01-21 00:38:42 +1000, Bob Badour <bbadour_at_pei.sympatico.ca> said:

> Joe Thurbon wrote:

>>
>> 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?

I see. So unless you do your counting and summing in a uniform manner you get complete nonsense. Which, I guess, might be achievable for this example, is pretty much intractable when the number or relations gets largish. And, as noted elsewhere, you really need one kind of null for each kind of 'missing', and that number will probably be at least as large as the number of attributes you have in all your relations.

>> 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.)

Is that paper available other than via the dbedebunk website? I understand that that site is no longer functioning. I think I saw, in my earlier readings, what looked like a slideshow involving column-wise and row-wise decompositions of null-addled relations: would that be the same thing?

> 
> 
>>> 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.

I'm glad to hear I'm not going to cause you to asphixiate! I've done a reasonable amount of research in the past - so I'm certainly not expecting to to come up with a complete treatment of missing information in my spare time. But thanks for the words of encouragement.

My general approach is really to see how tuples/relations in the RM map to logical statements. Then I can hopefully piggy-back off the wealth of research that has already happened in this area - it's "just" a matter of picking the right logic. But as I noted upthread, I'm mostly interested in this so that I feel I understand the RM relatively well. If I can contribute a little to the collective understanding, that would also be nice. I've got no illusions, though, I'm a late comer to a pretty well established field.

> 
> 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

[Aside] I've not seen this book before. It's funny how you can miss things: I did quite a lot of research into logical reasoning about knowledge; things like the AGM Belief Revision logics, Reiter's default logic, non-monotonic logics in general. I never came across it. I guess I wasn't as thourough as I had thought.

I had a look at the abstract, it certainly seems interesting. Thanks for the pointer.

> 
> 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.

I'll see if I can get it at a Library. I've still got some friends at some of the local universities.

Thanks again,
Joe Received on Sun Jan 21 2007 - 03:07:01 CST