Re: Interpretation of Relations

On 2007-01-23 03:13:38 +1000, "JOG" <jog_at_cs.nott.ac.uk> said:

>> 
>> Does any of this make any sense to you? To anyone?

Yes, I've been a little lazy with this up to now.

>
> As bob pointed out the relational algebra allows one to generate new
> propositions from those already stated, so this is the mechanism in
> which inferencing is performed.

I'm getting there eventually.

>
> The idea of incorporating modal logic is very interesting, but I'd note
> that give modal logic is reducible to first order logic (I sure I have
> read this but don't grill me on it),

I'm pretty sure this is not right. (It's been a while, though, but the semantics of modal logics seems richer than the semantics of FOL).

> there would be a response that RM
> is already capable of representing the desired results as is, and any
> extra layers provided to incorporate it would require careful thought
> indeed.
>
> For what its worth, I believe the crucical point is that the data model
> should not be trying to model facts from the real world, but rather our
> knowledge of those facts. This sounds like drivel to start with, but it
> does have an impact on representation:

It doesn't sound like drivel to me. (This may or may not be good news for you)

> Say we have a proposition from
> the real world, which has three roles x,y and z, and three
> corresponding values a,b and c. RM as it stands would represent this
> proposition directly as a tuple:
>
> P(x:a, y:b, z:c)
>
> whereas I believe a tuple should perhaps represent it 'indirectly' as
> a compound predicate:
>
> Exists p x(p,a) ^ y(p,b) ^ z(p,b)
>
> I believe the consequences of this subtle change in interpretation of
> what we are 'recording' (facts - or statements /about/ facts) _may_ be
> able to remove a lot of the logical errors generated by missing
> information, and perhaps some other issues too. But don't quote me on
> that.

I'm not sure exactly what the change in notation here is buying you. The formula still looks like facts, rather than statements about facts.

Regardless, my intuition is that a relational theory (by which I think I mean a set of relations) needs to be able to encode both types of statements. Sometimes your relations contain canonical data (say, in a payroll application), sometimes they encode observations (say, in our Hair example). But yes, I've written down a few possible logical interpretations of relations, and I often arrive at the Exists quantifier. But then I have all these existentially quantified variables, and I don't quite know what to do with them!

Anyway, I'll think about this more. I'm enjoying the conversation, so thanks.

Cheers,
Joe Received on Mon Jan 22 2007 - 22:57:13 CET