Re: NULLs: theoretical problems?

On 27 aug, 01:46, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
> 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 ?

Because the result of applying commutativity and associativity rules to a formula that is allowed might be a formula that is not allowed. For example, 'def(x) : x and y' might be rewritten to 'x and (def(x) : y)'.

> 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.

I've already defined when an allowed formula in the DEF logic is true and when not, so I'm not sure what more you want to hear from me.

• Jan hidders