# Re: NULLs: theoretical problems?

From: JOG <jog_at_cs.nott.ac.uk>
Date: Thu, 30 Aug 2007 12:08:10 -0000

On Aug 30, 10:02 am, Jan Hidders <hidd..._at_gmail.com> wrote:
> On 30 aug, 06:12, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
>
> > Jan Hidders <hidd..._at_gmail.com> wrote innews:1188272437.208915.202690_at_22g2000hsm.googlegroups.com:
>
> > > On 27 aug, 23:30, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
>
> > >> and we are forced to have the
> > >> 'def(x) :(x or not x)' which evaluates to 'false' ,
>
> > > That is not the only option. If you interpret the formula 'x' as 'x is
> > > defined and true' then the proper corresponding formula in DEF logic
> > > would be '(def(x):x) or not(def(x):x)' which of course evaluates to
> > > true.
>
> > Oh, man... You should have said it: '(def(x):x) or not(def(x):x)' at the
> > very beginning. We would have saved a lot of virtual trees !
>
> Stuff happens.
>
> > What you are proposing here is a Z crowd way to handle undefinedness,
> > one of many really.
>
> Of course. I never said it was something new, just that it was my
> favorite.
>
> > It's an old, very well know approach called "all
> > predicates denote" that some like and some others dislike. One of other
> > Z alternatives to do the same is of course a multi-valued Lukasiewicz-
> > like trick called LPF. You do not like LPF, I know. It does not have
> > LEM and deduction theorem, but LPF's expressivity with weak equality is
> > provably equivalent to "all predicates denote"/FOPC+existential equality.
>
> Sure, the expressive power in terms of what can and cannot be
> expressed is almost always the same and not really an issue. In fact,
> I would say it is besides the point.
>
> > Or something like that. Anyway, if I remember correctly, FOPC+exist.
> > eq. was criticised for being too verbose in expressing the same specs. as
> > LPF did, required two notions of equality, weak and existential, and
> > could not express complex predicates well. On the whole, it was a tie,
> > so in my mind neither was "better" than the other. Also, intuitively,
> > "all predicates denote" when some terms don't sounds rather fishy, don't
> > you agree ? How do you determine that a term does not denote,
> > practically speaking ?
>