Re: ?? Functional Dependency Question ??

From: paul c <>
Date: Tue, 21 Oct 2008 19:29:19 GMT
Message-ID: <j4qLk.3011$%%2.771_at_edtnps82>

David BL wrote:
> On Oct 22, 12:45 am, paul c <> wrote:

>> David BL wrote:
>>> On Oct 21, 11:54 pm, paul c <> wrote:
>>>> David BL wrote:
>>>> ...
>>>>> Consider that in the FD world symbol X represents a set of attributes
>>>>> from some relation R.  Let some tuple of R be given.  Then as a
>>>>> proposition we interpret X as implying that we are given or can deduce
>>>>> (for the given tuple) the values of all the attributes associated with
>>>>> X.   This interpretation makes it obvious that unions of attributes
>>>>> map to logical conjunctions, and that an FD maps to a logical
>>>>> implication.
>>>> Thanks, but how does that interpretation work when R has no attributes?
>>> What’s the problem?   If there are no attributes then the only FD we
>>> can state is
>>>     {} -> {}
>>> which is an example of a trivial FD (because rhs is a subset of the
>>> lhs).  In the propositional calculus this maps to
>>>    true -> true.
>>> The empty set of attributes (union identity) maps to true (conjunctive
>>> identity).
>> Okay, but isn't this changing the original mapping which was from VALUES
>> of attributes?

> I agree that as stated the interpretation isn’t very clear when R is
> empty – because it asks for a tuple of R to be given. Note also that
> I didn’t distinguish between intension and extension, and I understand
> that an FD has more to do with the former than the latter.
> By definition the empty set maps to ‘true’. This is consistent with
> saying that the proposition ‘true’ is interpreted as stating that for
> any given tuple the values of all the attributes in the empty set are
> knowable. This of course tells us nothing – as we expect from the
> information-less proposition ‘true’.

Thanks, that might have given me a clue for a slightly different mapping interpretation, (the old trick question "when there are no purple parts, which suppliers supply purple parts? answer is: all of them"). Received on Tue Oct 21 2008 - 21:29:19 CEST

Original text of this message