Re: ?? Functional Dependency Question ??

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’. Received on Tue Oct 21 2008 - 19:36:34 CEST