Re: A different definition of MINUS, part 4

From: paul c <toledobythesea_at_oohay.ac>
Date: Thu, 08 Jan 2009 16:14:00 -0800

```> 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.
>>
>> 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?
>

```

I'm not sure. By 'equals operation', I assume you mean equality test in an implemented language (as opposed to algebraic notation). 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. Received on Thu Jan 08 2009 - 18:14:00 CST

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