# Re: A different definition of MINUS, part 4

Date: Thu, 08 Jan 2009 21:30:56 -0400

Message-ID: <4966a8d1$0$5474$9a566e8b_at_news.aliant.net>

paul c 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?

*>*

> I'm not sure. By 'equals operation', I assume you mean equality test in

*> an implemented language (as opposed to algebraic notation).*

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.
*

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