Re: NULLs: theoretical problems?

"JOG" <jog_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:

>
> 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.

>

>
> There we are agreed.
>