Re: Interpretation of Relations

Joe Thurbon wrote:
> [snip]
> > 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.

Well comparing:
F1 = P(a, b, c)
F2 = Ep x(p,a) ^ y(p,b) ^ z(p,b)

I'd certainly consider F1 and F2 different propositions. F1 comments about the real world directly, whereas in a sense F2 is commenting about F1 (especially given it starts with existential quantifier, 'there is a proposition'). It also incorporates attribute names explicitly within the encoding (which seems to correspond to Codd's move to 'relationships' between the 1969 and 1970 paper pretty well) and it reflects the unordered nature of attributes in databases, given the conjunctions are commutative.

Either way, I think it would be more than a change in notation - the database is no longer expected to comment reliably on the real world, but rather just on what we know about the real world. If it stores one fact "I have been given a proposition that states Joes hair is Red", CWA over the database no longer implies that Joes hair is not black, but rather just that "I have not been given a proposition that states Joes hair is Black", saving me from any missing information contradictions.

As a logician perhaps you can tell me if the following makes any sense - to say Joe does have a hair colour and is not bald, I'd have: P = Ep Name(p, Joe) ^ Ey Hair(p, y).

Or to say Joe is bald:
P = Ep Name(p, Joe) ^ ~Ey Hair(p, y).

Or to say I don't know if I don't know if Joe is bald or not, well this is inferred from not saying anything at all.

There are other possible consequences in terms of being able to more advanced collectivizing of propositions but I'm nowhere on top of it (having to pay a mortgage and all), nevermind looking at the impact on the algebra . Ach well, Time will tell.

Until then I'll leave the modal logic in your hands.

>
> 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.

I look forward to seeing what conclusions you come up with. Regards, Jim.

>
> Cheers,
> Joe
Received on Tue Jan 23 2007 - 03:23:37 CET