# Re: ?? Functional Dependency Question ??

From: paul c <toledobythesea_at_oohay.ac>
Date: Tue, 21 Oct 2008 20:14:10 GMT
Message-ID: <mKqLk.3018\$%%2.33_at_edtnps82>

```> paul c wrote:
>
```

>> David BL wrote:
>>
>>> On Oct 22, 12:45 am, paul c <toledobythe..._at_oohay.ac> wrote:
>>>
>>>> David BL wrote:
>>>>
>>>>> On Oct 21, 11:54 pm, paul c <toledobythe..._at_oohay.ac> 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").
```>
> I think the answer is actually "none of them". If you changed the
> question slightly to "When there are no purple parts, which suppliers
> supply all of the purple parts?" then the answer would be "all of them".
>

```

Right.

thanks Received on Tue Oct 21 2008 - 22:14:10 CEST

Original text of this message