Re: Constraints and Functional Dependencies

Keith H Duggar wrote:
> mAsterdam wrote:

>> A rephrase to (i) could be:
>>
>> <reference>
>> (i a)
>>    A relation R with attribute a (written as R(a)) having
>>    a as a reference into S(b)
>>    is expressed as follows:
>>
>>    forall R(a): exists S(b): a = b
>>
>>    Note that b need not be a ck to S, hence 'into', not 'to'.
>> </reference>

In the OP Marshall wrote:
 > With such a system, a relation R with  > attribute a (which I will write as R(a))

where he could have written

 > With such a system, a relation R with  > *only* attribute a (which I will write as R(a))

if he'd wanted R(a) to denote a relation with only one attribute a. Marshall knows; ask him.

If you read the subsequent discussion you'll agree that it cannot be assumed that b must be S's only attribute.

> If so then b is necessarily a ck (in fact the only key).

Of course. But then several subthreads (contributions by paul c, Cimode and Marshall) would be irrelevant. I am sure Marshall would have had the courtesy to point that out.

> If S(b) is actually a shorthand notation for
> S(b,b0...bn) then one can express that b is a ck by:
>
> forall b: exists c0,...cn: forall b0...bn:
> S(b,b0...bn): b0 = c0 ... bn = cn
>
> Correct?

In Marshall's notation that would be
{b} -> {b0,...bn} =def=

     forall S(b, b0,...bn): forall S(b, b0'...bn'):
        b=b' => b0 = b0' ... bn = bn'

I think.

Note that for instance "exists c0,...cn:" simply disappears, because of

> We can use the existing attribute
> names as the names of the logic variables.

, a chosen ambiguity I already pointed out: P(a) denotes both 'P has an attribute a' as well as a value for a.

This is just how I understood it.
To be sure you shouldn't ask me. Received on Sun Feb 25 2007 - 18:40:09 CET