Re: Columns without names

vc wrote:
> JOG wrote:
> [..]
> > Imagine, f'rinstance, I have a data collection in which I have
> > propositions of dogs' names & ages and owners' names & ages. Both sets
> > of propositions would traditionally be represented as (name:x, age:y),
> > but yet are housed in separate relations to form my manipulable
> > datatbase. How exactly has this been determined by the set intension?
>
> What's a "set intension" ?

An intension defines what a set consists of. e.g.:

S = {x E N : x<10 }
S = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

are the same things. the first written intensionally (x is a natural number less than 10), the second extensionally, but AFAIK its always one way or the other.

> Is it the same thingy as the predicate
> defining some set ? If yes, why not say so ?

No not exactly. The intension of a set of tuples may be viewed as a predicate such as P(id, name, age) combined with constraints, but in that format it can be difficult to encode as one logical statement. So given a data collection as a whole is a hotch potch of different asserted statements, I've been consdering viewing a proposition, x, as a relationship between attributes and values, so you could say something like:

S = { x: Ea Name(x, a) & Eb Age(x,b) }
(E representing the existential operater 'there exists' here)

but also combine it with a constraint that age must be more than 18 say...

S = { x: Ea [ Name(x, a) ] & Eb [ Age(x,b) & b>18 ]}

Don't get me wrong, I'm just exploring this stuff. It doesn't affect the RM in any way as far as I can see, it's just offers me a mathematically pleasing way of writing the makeup of a relation down.

> The "set intension"
> expression is hard, if not impossible, to find in any decent
> predicate logic/math book that one might be familiar with.

Quite the opposite vc. The concept of intension is one of the basic grounding blocks of set theory, and will be detailed in any beginners set theory text book in the first couple of chapters. Its a bog standard way of defining sets. Received on Tue Sep 19 2006 - 21:37:18 CEST