Re: NULLs: theoretical problems?

From: V.J. Kumar <vjkmail_at_gmail.com>
Date: Sun, 26 Aug 2007 16:46:22 -0700
Message-ID: <1188171982.017564.166660@r29g2000hsg.googlegroups.com>

Jan Hidders wrote:
> On 25 aug, 16:39, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
> > Jan Hidders <hidd..._at_gmail.com> wrote innews:1188037788.486939.308150_at_i38g2000prf.googlegroups.com:
> >
> >
> >
> > > On 25 aug, 02:13, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
> > >> Jan Hidders <hidd..._at_gmail.com> wrote
> > >> innews:1187998409.227306.271460_at_e9g2000prf.googlegroups.com:
> >
> > >> > On 24 aug, 16:35, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
> > >> >> You may be right, but then why the formula was not written with
> > >> >> an explicit 'and' ?
> >
> > >> > Because it does not satisify all the logical laws of an AND, so to
> > >> > avoid confusion another notation is used.
> >
> > >> What logical laws of AND are violated when we interpret
> >
> > >> 'def(x):f(x)' as 'def(x) and f(x)' ?
> >
> > > Commutativity and associativity.
> >
> > What "Commutativity" ?
> >
> > Does not 'f(x) and def(x)' evaluate to the same as 'def(x) and f(x)'
> > would where def(x) is interpreted as a definedness predicate ?

>

> Assuming that your are working in some 3VL so f(x) is defined, yes, it
> probably does.

It should be blindingly obvious that I meant your DEF logic. I'll say it again: does not 'def(x) and f(x)'' commute in your logic if def(x) is understood as a definedness predicate and if the answer is "no", why it doesn't commute ?

>


> > What "associativity" ?

> >

> > Does not 'def(x) and (x or y)' evaluate to the same as 'def(x) and x or

> > def(x) and y' would where def(x) is interpreted as a definedness
> > predicate ?

>

> Yep.

>

> And it is exactly to avoid the impression that something like this
> would hold for the DEF construct that a distinct notation is used.

Why the Def(x) construct cannot be interpreted as a definedness predicate ? If you claim that the DEF logic is almost if not exactly 'the same' as the classical first order logic, then what exactly is Def in your logic ? Please no handwaving, just give a formal definion and show why you need to introduce a new construct which is not a predicate.
>
> -- Jan Hidder
Received on Sun Aug 26 2007 - 18:46:22 CDT