Re: NULLs: theoretical problems?

On 24 aug, 06:03, Keith H Duggar <dug..._at_alum.mit.edu> wrote:
> Jan Hidders wrote:
> > V.J. Kumar wrote:
> > > Jan Hidders wrote:
>
> > > > I mean that if you take a select-from-where query with a formula f in
> > > > in the where clause containing the DEF construct then replacing f with
> > > > f' where all the DEF constructs are removed (i.e. we replace "DEF x :
> > > > g" with "g" until there are no more such expressions) sometimes
> > > > changes the meaning of the query.
>
> > > Let's take a look at it. Could you give a query example and you
> > > interpretration of the DEF construct therein ?| ?
>
> > SELECT * FROM t WHERE DEF t.a : (t.a = 5 OR TRUE);
>
> > is not equivalent with
>
> > SELECT * FROM t WHERE t.a = 5 OR TRUE;
>
> > I'm not sure why you want me to explain the meaning of the DEF
> > construct again, because you already seemed to understand it, but for
> > completeness: the formula "DEF c : f" holds iff the value of column c
> > is defined and the formula f holds.
> And previously you wrote:
> > meaning of "DEF t.a : f(t.a)" would be that t.a is defined and the
> > formula f(t.a) holds. It would be required for nullable attributes,
> > but not for not nullable attributes. So if t.a is nullable, and s.b
> > not, then you would have to write "DEFI t.a : t.a = s.b". The need for
> > this can be relatively straightforwardly checked by the DBMS
>
> So it's required to "write DEF" for all nullable attributes

Exactly.

> and a
> formula is true only if the nullable attributes are defined.

That case is avoided because the formula only has to be evaluated if all nullable attributes in it are in fact defined.

> How
> is this different from dropping the requirement to "write DEF" and
> simply defining that a formula is false if any of it's variables
> is undefined?

Then some of the basic laws of propositional logic would no longer hold. For example "P OR NOT(P)" would not be always equivalent ot "TRUE" since the first might contain a nullable attrbute and therefore be sometimes false under your interpretation, and the second of course never is. Or what would be the result of NOT(NOT(P)) if P contains an undefined variable? False? But the result of NOT(P) is also false. So NOT(false) = false?

• Jan Hidders