Re: NULLs: theoretical problems?

On Aug 31, 2:13 am, Jan Hidders <hidd..._at_gmail.com> wrote:
> On 30 aug, 14:08, JOG <j..._at_cs.nott.ac.uk> wrote:
>
>
>
> > 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.
>
> I'm sorry to say that at the moment I cannot tell you where I got it.
> The thing that comes closest is Beeson's logic of partial terms, which
> has an explicit definedness operator for terms. But it lacks the idea
> of a syntactic restriction that allows you to keep the normal
> reasoning rules of FOL.

"The Foundations of Constructive Mathematics" is not an easy book to get hold of...

>
> Btw. while looking for that I did find in comp.theory a list of
> references on logics dealing with undefinedness. It's probably not
> useful to you because more than you asked for, but I'm giving it
> anyway:
>
> http://groups.google.com/group/comp.theory/msg/884efa5e74a5f68e

thanks for these. Much appreciated.

>
> Of course, if you really want a formal reference I might consider
> writing a small technical report about it. ;-)

I think you should make this a priority! Oh, and don't forget to mention me in the acknowledgements as a motivating factor in its generation ;)

>
> Kind regards,
>
> -- Jan Hidders

"...not even with these (contraries 'Socrates is well' and 'Socrates is sick') is it necessary always for one to be true and the other false. For if Socrates exists one will be true and the other false, but if he does not both will be false... " (Aristotle, Categories, x, 13b12)

Its good to know we've only been thinking about these concepts for 2300 years... Received on Fri Aug 31 2007 - 17:21:19 CEST