Re: NULLs: theoretical problems?

From: V.J. Kumar <vjkmail_at_gmail.com>
Date: Fri, 31 Aug 2007 18:55:45 +0200 (CEST)
Message-ID: <Xns999D83900C0D9vdghher@194.177.96.26>

Jan Hidders <hidders_at_gmail.com> wrote in news:1188523367.163903.141220 @m37g2000prh.googlegroups.com:

> On 30 aug, 06:12, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:

>>
>> What you are proposing here is a Z crowd way to handle undefinedness,  
>> one of many really.  It's an old, very well know approach called "all
>> predicates denote" that some like and some others dislike.

>
> As far as I can see it isn't. I first thought you were right, (hence
> my previous reply, although I'm still not claiming this is something
> original) but since Jim asked me about it I read it back, and as far
> as I can tell they don't have a corresponding notion of syntactical
> restriction which is pretty much at the core of the approach I'm
> talking about. So could you give a concrete reference and maybe a
> short explanationa of why you think it is the same?

Your current disagreement plus, especially, your talking about noncommutativity  prodded me to strain my memory and recall a real fossil, some book by Gries, or Dijkstra or both. He/they wrote it when I was probably in the kindergarten. Anyway, he used those non-commutative 'cand', 'cor' and so forth to "guard" against undefined values:

'defined(x) cand MyPredicate(x)'

gives exactly what you wrote about including this nice non-commutativity plus some other gems like need to have two packs of connectives, the normal ones plus the conditional beasts. So, yes, I was wrong, your ideas are perhaps closest/the same to/as the cand/cor/etc stuff.

In comparison to "conditionals", partial logic is a thing of beauty since it is almost classical predicate calculus with weird equality or definednes predicate. No need to kill commutativity or anything like that.

IMNSHO, partial logic is still worse than a three-valued way for undefinedness for the reasons I mentioned earlier.

>
> -- Jan Hidders
>
Received on Fri Aug 31 2007 - 11:55:45 CDT