# Re: ?? Functional Dependency Question ??

Date: Tue, 21 Oct 2008 09:37:55 -0700 (PDT)

Message-ID: <01af9f4f-8ec1-4112-b8fa-8c3ed6f6769f_at_w39g2000prb.googlegroups.com>

On Oct 22, 12:16 am, Tegiri Nenashi <TegiriNena..._at_gmail.com> wrote:

> On Oct 21, 8:40 am, David BL <davi..._at_iinet.net.au> wrote:

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**> > On Oct 21, 10:22 pm, paul c <toledobythe..._at_oohay.ac> wrote:
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**> > > David BL wrote:
**> > > > On Oct 21, 8:15 pm, paul c <toledobythe..._at_oohay.ac> wrote:
**> > > >> David BL wrote:
**>
**> > > >> ...
**>
**> > > >>> RTP: (X->A)(Y->B) -> XY->AB
**> > > >>> (X->A)(Y->B) : premise
**> > > >>> X->A, Y->B : conjunction elimination
**> > > >>> XY : premise
**> > > >>> X,Y : conjunction elimination
**> > > >>> A : modus ponens on X,X->A
**> > > >>> B : modus ponens on Y,Y->B
**> > > >>> AB : conjunction introduction
**> > > >>> XY->AB : conditional proof
**> > > >>> (X->A)(Y->B) -> XY->AB : conditional proof
**> > > >> I can see that the second step is eliminating a "conjunction" but the
**> > > >> fourth step doesn't seem to me to involve a conjunction.
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**> > > > Step 3: Premise XY (the conjunction of X and Y).
**>
**> > > ...
**>
**> > > But XY (in the usual FD notation) is a union, not a conjunction.
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**> > > (If step 4 is valid, there must be a subtlety here that goes beyond just
**> > > conjunction elimination, ie., some other notion must be involved, but so
**> > > far it could be eludes me.)
**>
**> > Ah, Ok I understand your point now. (X->A)(Y->B) -> XY->AB is a
**> > formula in the propositional calculus, which is shown to be a
**> > theorem. In that context XY is definitely a logical conjunction.
**>
**> > In FD notation we think of X,Y as sets of attributes and as you say XY
**> > is a notation for the union of those sets. However there is this
**> > idea of translating an FD sentence into a formula in the propositional
**> > calculus. This mapping can be done as follows
**> > - sets of attributes can be mapped to proposition symbols
**> > - unions of sets of attributes can be mapped to logical conjunction
**> > - a functional dependency can be mapped to a logical implication
**>
**> > 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 perspective of FD theory into propositional calculus is new to
**> me. So could you please be more specific? Sure propositional calculus
**> has some axioms that have no interpretation in FD world, e.g.
**>
**> A -> (B -> A)
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**> or it has?
*

I would say wff’s of FD theory map to a strict subset of wff’s of the propositional calculus.

The idea is not mine. I’m trying to make sense of Bob Badour’s post where he suggested a simple connection between FD and logical implication. Received on Tue Oct 21 2008 - 18:37:55 CEST