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Re: All hail Neo!

From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Sun, 23 Apr 2006 13:58:14 GMT
Message-ID: <WJL2g.64598$VV4.1223196@ursa-nb00s0.nbnet.nb.ca>


Frank Hamersley wrote:

> Bob Badour wrote:
>

>> Frank Hamersley wrote:
>>
>>> Bob Badour wrote:

>
> [..]
>
>>>> In that line of thought, here's an interesting question that Date et 
>>>> al have posed before to the n-VL folks:
>>>>
>>>> If "exists but empty" is true and "doesn't exist" is false, what is 
>>>> null?
>>>
>>> Neither and both!
>>
>> I find that sort of handwaving to be a complete non-answer.

>
> I suspect you are wearing the darkly tinted glasses of preconception.
> Whilst I was trying to show a little wit, the current 3VL state of
> affairs still seems to me to fit that description.
>
>> A much more intellectually honest reply would be: "I don't know."

>
> Not from this black duck (on this occasion)!
>
>> or "Null has no similar analog in set theory."

>
> I wasn't comparing/contrasting the RM with set theory. Perhaps for you
> it is implicit?

No, it is quite explicit. Relations are sets. Relational algebra is the equivalent of set theory, and relational calculus is the equivalent of predicate calculus.

Thus, the equivalence of dee and true and of dum and false are very important. And the question of what relation value equates to null is a very good question.

>> True and 1 both have the exact same analog in set theory. False and 0 
>> both have the exact same analog in set theory.

>
> Perhaps but insistence on a parallel form for the RM does not seem to
> lead anywhere practical*...FWICT.

Are you suggesting that query transformations lack practical benefits?

>> This has a certain elegance and symmetry.

>
> I agree that and readily subscribe to that in my own endeavours.
>
>> In canonical form:
>>
>> {} = 0 = false
>> {{}} = 1 = true
>>
>> What is the similar analog for null?

>
> My prior knowledge of your/the notation is non existent but I can prolly
> deduce its intent. So having a stab at it how about ...
>
> {}{} = null

{} is the empty set and is the set with cardinality 0. {{}} is the set containing an empty set and is the canonical form of all sets with cardinality 1.
{{},{{}}} is the canonical set with cardinality 2. http://www.math.psu.edu/simpson/papers/philmath/node17.html

One can continue in this vein until Goedel stomps on one. http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

With respect to {}{} either it is completely meaningless, or perhaps you intend the juxtaposition of two sets to mean conjunction or disjunction, in which case:
{}{} = {} = false

If null and false are the same, we can do away with null.

> As an aside (and with no malice aforethought) I am curious why the 0 and
> 1 figure at all? Forced to conform I would probably go with ...
>
> {}{} = -1 = null

0 and 1 figure by tying into the formalism for whole numbers as shown above. http://en.wikipedia.org/wiki/Foundations_of_mathematics

I direct your attention to:
http://en.wikipedia.org/wiki/Formalism#Mathematics

"Complete formalisation is in fact in the domain rather of computer science."

And finally, the relational model is itself a formal system:

http://en.wikipedia.org/wiki/Formal_system

See also:
http://en.wikipedia.org/wiki/Category:Mathematical_logic

> * (for another post perhaps) I don't see any great leap forward in the
> aspects of TTM that address the extinction of nulls.

If nulls cause great damange without serving any particularly useful purpose, why should one address their extinction? Received on Sun Apr 23 2006 - 08:58:14 CDT

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