Re: A different definition of MINUS, part 4

paul c wrote:

> Bob Badour wrote:
>

>> paul c wrote:
>>
>>> Cimode wrote:
>>>
>>>> On 28 déc, 14:56, paul c <toledobythe..._at_oohay.ac> wrote:
>>>> [Snipped]
>>>> <<I'm not sure that this is anything really different from saying that
>>>> we want logical consistency to be demonstrable in a dbms
>>>> implementation>>
>>>> It can not be done without estalishing valid quantifiers for algebric
>>>> expression or for non algebric expression of RL equations to be
>>>> resolved.  This is one of the aspects I have been trying to underline
>>>> in previous posts and that is a prerequisite to design a computing
>>>> model that may allow closure for implementation.  In the case of
>>>> algebric expressions of RL, distance is the most obvious quantifier
>>>> one can use.  But D&D as well as Mc Goveran seem to ignore it.
>>>>
>>>> Regards and Merry Christmas to you.
>>>
>>>
>>> Thanks, mutual.  One thing I don't understand about your quantifier 
>>> comment; if an algebra has a projection operator, don't we have 
>>> quantification in the algebra?  (ie., "Exists"?)
>>
>>
>> I don't understand Cimode's comment either, but it occurs to me that 
>> the equals operation for relations provides both quantifiers. 
>> Projecting on zero attributes and comparing with DEE gives EXISTS and 
>> comparing with a full relation of some sort gives ALL.
>>
>> Am I missing something?

No, not necessarily. R1 = R2 is fine in algebraic notation, is it not?

   Logically,
> I assumed that an algebraic definition of Forall is possible since
> projection is the 'counterpart' of exists and since negation is allowed
> in the algebra. In the 1972 paper, Codd said his Divide was a
> counterpart to the universal quantifier, but I gather not a complete
> counterpart since Date talks about problems when its operands are empty
> relations. Personally, I've never had to find suppliers who supply all
> purple parts when there were no purple parts, but a couple of times my
> eyes couldn't stay focussed when I tried to write the equivalent of
> relational division in SQL. If ever a language needed a shorthand that
> would be one. I think a lot of times, the right answer can be got
> without Forall, as long as we have projection. I gather that 'full
> relation' often means a cartesian product.

Just a relation expressing all of what all is. In the suppliers/parts example, one might group parts from SP into a relation valued attribute and then compare that against the P relation projected on {P}

I am unsure of the exact notation but something like:

(SP{S,P} GROUP Parts{P} | Parts = P{P}){S} Received on Fri Jan 09 2009 - 02:30:56 CET