# Re: NULLs: theoretical problems?

Date: Thu, 30 Aug 2007 09:02:36 -0000

Message-ID: <1188464556.667227.173720_at_19g2000hsx.googlegroups.com>

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 ?
*

Since you know so much about it, I assumed you had already guessed. :-)

- Jan Hidders