Re: Codd's Information Principle
From: paul c <toledobythesea_at_oohay.ac>
Date: Sat, 07 Nov 2009 03:30:05 GMT
Message-ID: <1R5Jm.50872$Db2.673_at_edtnps83>
>
> 'R(x,1)' is a result of substituting y=1 into R(x,y). This is
> literally the same trick as substituting n=1 in the term x^(-n) which
> is a part of summation
>
> sigma( n={1...inf} , x^(-n) )
>
> We simply substituted sigma with "exists", bind variable n with y, and
> left x as free variable in both cases. Moreover, many math books use
> the big disjunction symbol "\/" for "exists" in order to emphasize the
> idea that existential quantification is merely repeated application of
> binary disjunction.
Date: Sat, 07 Nov 2009 03:30:05 GMT
Message-ID: <1R5Jm.50872$Db2.673_at_edtnps83>
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. Why don't you just use tuple literals for your development? In any event, I don't see how you can avoid a projection operator which I don't believe can be defined in terms of the other D&D ops. Received on Sat Nov 07 2009 - 04:30:05 CET