Re: Codd's Information Principle

On Nov 6, 7:30 pm, paul c <toledobythe..._at_oohay.ac> wrote:
> Tegiri Nenashi wrote:
> > On Nov 6, 5:08 pm, paul c <toledobythe..._at_oohay.ac> wrote:
> >> Tegiri Nenashi wrote:
>
> >> ...
>
> >>> Likewise, relational calculus quantified expression
> >>> exists y : R(x,y)
> >>> is essentially a disjunction
> >>> R(x,1) <OR> R(x,2) <OR> R(x,3) <OR> ...
> >>> ...
> >> In the spirit of the recent precision, it doesn't look to me like
> >> 'R(x,1)' et cetera are sets of tuples, which I believe '<OR>' requires.
> >>   Shouldn't that '<OR>' be logical 'OR'? Also the result doesn't look
> >> 'truth-valued', shouldn't it?
>
> >  'R(x,1)' is a result of substituting y=1 into R(x,y). This is
> > literally the same trick as substituting n=1 in the term x^(-n) which
> > is a part of summation
>
> > sigma( n={1...inf} , x^(-n) )
>
> > We simply substituted sigma with "exists", bind variable n with y, and
> > left x as free variable in both cases. Moreover, many math books use
> > the big disjunction symbol "\/" for "exists" in order to emphasize the
> > idea that existential quantification is merely repeated application of
> > binary disjunction.
>
> To say that '<OR>' operates with free variables looks like a flight of
> fancy to me. You'll have to substitute out the 'x' too if you want to
> use '<OR>' or come up with a new definition for it, otherwise you're
> just usurping it to apply to something other than tuples.  

OK, I shouldn't have written <OR> (to avoid any confusion caused by reference to D&D "A"lgebra). It was meant to be iterative disjunction of unary predicates

R(x,1) v R(x,2) v R(x,3) v ...

each obtained from binary predicate R(x,y) by formal substitution of free variable y with constant. (From RA perspective this substitution is projection indeed, but this idea is unnecessary -- everything was meant to be explained in predicate calculus terms). Received on Sat Nov 07 2009 - 04:57:53 CET