Re: NULLs: theoretical problems?

On Aug 13, 11:42 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> "JOG" <j..._at_cs.nott.ac.uk> wrote in message
>
> news:1187008163.120347.20000_at_22g2000hsm.googlegroups.com...
>
>
>
> > On Aug 13, 1:06 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> >> "JOG" <j..._at_cs.nott.ac.uk> wrote in message
>
> >>news:1186971690.979746.159320_at_l70g2000hse.googlegroups.com...
>
> >> > On Aug 8, 11:43 am, "sinister" <sinis..._at_nospam.invalid> wrote:
> >> >> Many discussions point out one deficiency of NULLs: that they
> >> >> collapse
> >> >> multiple, distinct concepts into one ("no value possible," "value
> >> >> missing,"
> >> >> "value not available at this time", etc).
>
> >> >> What are the other theoretical problems? My impression from skimming
> >> >> some
> >> >> threads in this ng is that some anomalies might occur, maybe having to
> >> >> do
> >> >> with NULLs and joins, or NULLs and keys composed of more than one
> >> >> field,
> >> >> but
> >> >> I'm not sure.
>
> >> > A database stores true propositions. A statement with a hole in it (an
> >> > SQL null) is not a proposition, and hence is a theoretical abhorrence.
>
> >> Not necessarily. If there can always be a value for an attribute, but it
> >> simply hasn't been supplied, then the "hole" isn't a hole, but rather a
> >> disjunction that means one of the values in the domain for the attribute.
> >> The statement is therefore a true proposition, even if it is
> >> indeterminant.
>
> > I disagree, even in that situation propositions can't have holes or
> > gaps according to relational theory. If one is kludging in a flag that
> > means "one of the values from the domain", one is in fact trying to
> > state something completely different using the existential quantifier.
> > And that will make it a predicate not a proposition due to the
> > inclusion of "metadata" (for want of a better term). For example:
>
> > Name(Tom) ^ Age(38) ^ Ex HairColour(x)
>
> > or if you don't want to include attribute names:
> > Ex Person(Tom, 38, x)
>
> > which is entirely different kettle of fish from:
> > Person(Tom, 38, brown)
>
> > The former is a statement in FOL, the latter a statement in
> > propositional logic. In RM only the relation is predicated, with
> > tuples satisfying that predicate, and hence the null flag is
> > theoretically and mathematically incorrect.
>
> The thing is that the existential quantifier isn't correct in this instance,
> due to the entity integrity rule which states that there must be a value for
> every prime attribute. As a result, the correct quantifier is exists! x,
> rather than exists x, which means "there is one x" rather than "there is at
> least one x." For finite domains, there is a fixed interpretation for the
> quantifier exists!. For example, assuming that the domain for HairColour
> is {blond, red, brown, black}, then the formula
>
> exists! x Person(Tom, 38, x) becomes,
>
> Person(Tom, 38, blond) /\ ~Person(Tom, 38, red) /\
> ~Person(Tom, 38, brown) /\ ~Person(Tom, 38, black) \/
> ~Person(Tom, 38, blond) /\ Person(Tom, 38, red) /\
> ~Person(Tom, 38, brown) /\ ~Person(Tom, 38, black) \/
> ~Person(Tom, 38, blond) /\ ~Person(Tom, 38, red) /\
> Person(Tom, 38, brown) /\ ~Person(Tom, 38, black) \/
> ~Person(Tom, 38, blond) /\ ~Person(Tom, 38, red) /\
> ~Person(Tom, 38, brown) /\ Person(Tom, 38, black)
>
> And, yes, it is a different kettle of fish than
>
> Person(Tom, 38, brown)
>
> which is not only positive but also definite. But still the indefinite
> proposition is a positive proposition. Note also that the definite
> proposition implies the indefinite one. The main difference between this
> interpretation and one that replaces each occurrence of null with a
> different free variable is that the indeterminant proposition is true (under
> an interpretation), whereas an atomic formula with a free variable can be
> neither true nor false until a value is assigned.

Well put. I see what you are saying and I think you are right about uniqueness quantification.

>
>
>
> >> > Or from a different angle you might want to consider that a relation
> >> > is a set of tuples. A tuple must contain a value in every position, or
> >> > it is not a valid tuple (not being a subset of the cartesian product
> >> > of the domains being considered). Hence an SQL-null is a theoretical
> >> > abhorrence.
>
> >> I wouldn't say that it is not a valid tuple, but rather that the set of
> >> tuples is no longer strictly a relation. A tuple is simply a set of
> >> named
> >> values, but a relation in its strictest sense is a named set of tuples
> >> that
> >> each have one value for each of the attributes in the heading. As can
> >> easily be seen above, the lack of regularity is not necessarily a
> >> problem,
> >> unless there are instances where there cannot be a value for an attribute
> >> in
> >> each tuple. I therefore wouldn't call it a "theoretical abhorrence," but
> >> rather a more concise way to represent the same information. There can
> >> be
> >> merit in a more concise representation, not the least of which is the
> >> reduced computational complexity (big-O) for both queries and updates.
>
> >> I do agree that the 3VL involving SQL-null is definitely broken.
>
> > There we are agreed.
>
> >> > The solution is of course to decompose a relation around its key so
> >> > that no nullable columns are required. This results in a schema with
> >> > more relations, and tends to produce queries with more joins, but
> >> > without any theoretical or logical flaws.
>
> >> > Some view such decomposition as being computationally inefficient,
> >> > others reply that this is a physical implementation issue and not a
> >> > concern of the logical model.
>
> >> > Given the fact that it can generate much longer queries, I sometimes
> >> > find myself allowing nulls in personal home-brew projects out of sheer
> >> > laziness. However I do suffer from internal pangs of guilt during the
> >> > process ;)
Received on Tue Aug 14 2007 - 17:25:19 CEST