Re: Columns without names

vc wrote:
> JOG wrote:
> > vc wrote:
> [...]
> > > 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.
>
> So what would be an "set intension" example which is not a predicate ?
> The above clearly does not qualify.

S = { x : x = x^2)

0 and 1.

But I gather your point. The reason I use a different terminology is because in RM the use of the term predicate, traditionally refers to an atomic form such as P(a,b..c) and not a compound predicate.

>
>
> >
> > > 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.
>
> Could you kindly supply a mathematical set theory textbook reference
> that would use such bizzare terminology in preference to commonly
> accepted FOL language ?

bizarre? formal you mean. http://mathworld.wolfram.com/Intension.html Received on Wed Sep 20 2006 - 01:06:32 CEST