Re: Interpretation of Relations

From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Sat, 20 Jan 2007 14:38:42 GMT
Message-ID: <SPpsh.3100$1x.53429@ursa-nb00s0.nbnet.nb.ca>

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. Received on Sat Jan 20 2007 - 08:38:42 CST