# Re: NULLs: theoretical problems?

Date: Thu, 30 Aug 2007 12:08:10 -0000

Message-ID: <1188475690.022985.280440_at_22g2000hsm.googlegroups.com>

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 ?
**>
**> Since you know so much about it, I assumed you had already
**> guessed. :-)
**>
**> -- Jan Hidders
*

I use a similar notion to def in my own work, but am lacking any references for it. You say that it is an established (or at least recorded) approach - do you have links to texts, or academic references? Or does it have a more formal nomenclature that I could search for > my normally leet googling skills are not serving me well. Many thanks, Jim. Received on Thu Aug 30 2007 - 14:08:10 CEST