Oracle FAQ | Your Portal to the Oracle Knowledge Grid |
Home -> Community -> Usenet -> comp.databases.theory -> Re: All hail Neo!
Frank Hamersley wrote:
> Bob Badour wrote:
>
>> 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.
Yes, ALL relations are sets of tuples. SQL tables are not relation variables and do not contain relations.
My gut feeling is that this is not true. I
> recognise that I hold to this because I view it from the damaged goods
> position (aka SQL) or the RM as propounded by Codd, rather than from a
> sounder theoretical starting point.
RM/V2 seems flawed to me. I am not sure whether I have ever found a complete copy of RM/T. Did Codd ever advocate null prior to RM/T? Did he ever drop the requirement for logical identity?
I understand this puts us at odds
> from inception. From there I expect anything brought to this issue by
> theory will be elegant, symmetrical _and_ compelling.
Relations are elegant, symmetrical and compelling. Bags and null are none of those.
> [2nd editing]
> Having read the texts, below I felt inclined to retract the above para,
> but then decided to leave it so you could form your own view on how
> wacky my thinking might be. That said perhaps the fact that nulls do
> exist in the RM today taken with your confirmed view that they shouldn't
> (from a theoretical basis) is implied confirmation of my rather unlikely
> original thought...he says stepping back two full paces - did I write that?
Whether nulls exist in the RM today is a topic of some controversy.
>> Relational algebra is the equivalent of set theory, and relational >> calculus is the equivalent of predicate calculus.
With null or without logical identity, they lack the equivalences mentioned.
>> 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.
Shall we get back to this now?
>>>> 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?
The equivalence between relation values and boolean values facilitates certain query transformations such as between a union and an 'or' predicate and vice versa.
>>>> 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
Goedel established limitations to formalism as the foundation of mathematics, and I am not sure that philosophy is meant to have an endpoint.
>> One can continue in this vein until Goedel stomps on one. >> http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
LOL
>> 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
One wonders in what way they are distinct. Is 1 distinct from 1? Is 0 distinct from 0? Obviously, as values, they are indistinct. One must then posit that they differ in location. However, a single attribute within a single tuple within a single relation variable has a unique logical location. How then can null equate to two locations? What then does it mean when the null appears in a derived value which has no location at all?
>> If null and false are the same, we can do away with null.
If null is not the same as false, then it is not the same as {}. Does it then have an equivalent set representation?
>>> 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
I suspect your statement is true of all of mathematics and in fact of all fields of study.
>>> * (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?
Are you familiar with Date's various _Writings..._ books? He and Darwen and others have demonstrated that null causes great damage.
Nulls attempt to address missing information but do so with no basis in theory. I suggest that the null elixir only offers the illusion of power: http://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD898.html
As to
> Date and Darwens attempt to remove nulls as shown in the Tutorial-D
> slides it didn't seem to meet the elegance or compelling stature I
> mentioned before.
Missing information is messy, and we lack any theory to address it. Pretending otherwise may put the mess out of sight and out of mind, but that just makes the mess worse and the problems more surprising when re-discovered. Received on Mon Apr 24 2006 - 11:00:39 CDT