Re: NULLs: theoretical problems?

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.

> 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.

• Jan Hidder