Re: NULLs: theoretical problems?

Jan Hidders <hidders_at_gmail.com> wrote in news:1188272437.208915.202690_at_22g2000hsm.googlegroups.com:

> On 27 aug, 23:30, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:

>> In addition to  the de  facto loss of the 'x
>> or not x' tautology when x is undefined

Sure I do, but it is not the one that is relevant to the discussion.

> As you already yourself
> indicate it is highly debatable whether this is a tautology at all, so
> I'm not sure why you bring it up.

You did it first when you complained about the three-valued logic ;)

>

>> and we are forced to have the
>> 'def(x) :(x or not x)'   which evaluates to 'false' ,  

Oh, man... You should have said it: '(def(x):x) or not(def(x):x)' at the very beginning. We would have saved a lot of virtual trees ! I thought your idea was to guard an entire formula with the def construct, and that you were not allowed to mix the def thingies inside formulas. That's what got me interested.

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. One of other Z alternatives to do the same is of course a multi-valued Lukasiewiczlike  trick called LPF. You do not like LPF, I know. It does not have LEM and deduction theorem, but LPF's expressivity with weak equality is provably equivalent to "all predicates denote"/FOPC+existential equality. Or something like that. Anyway, if I remember correctly, FOPC+exist. eq. was criticised for being too verbose in expressing the same specs. as LPF did, required two notions of equality, weak and existential, and could not express complex predicates well. On the whole, it was a tie, so in my mind neither was "better" than the other. Also, intuitively, "all predicates denote" when some terms don't sounds rather fishy, don't you agree ? How do you determine that a term does not denote, practically speaking ?

>> There are also some negative
>> practical implications with the blanket evaluation of the formulas
>> containing at least one variable that may happen to be undefined to
>> 'false', but we'll talk about that next time.

I'll have to disappoint you ;). I'm not interested very much in the "existential" FOPC and do not have anything to add. I regard it as essentially a language, not much different from the three valued SQL logic when dealing with undefinedness.

>
> -- Jan Hidders
>
>
Received on Thu Aug 30 2007 - 06:12:47 CEST