# Re: ?? Functional Dependency Question ??

Date: Tue, 21 Oct 2008 16:45:48 -0300
Message-ID: <48fe317f\$0\$5491\$9a566e8b_at_news.aliant.net>

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").

```

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