Re: NULLs: theoretical problems?
From: Jon Heggland <jon.heggland_at_idi.ntnu.no>
Date: Sun, 26 Aug 2007 10:12:25 +0200
Message-ID: <farcle$ars$1_at_orkan.itea.ntnu.no>
>
> What "Commutativity" ?
>
> Does not 'f(x) and def(x)' evaluate to the same as 'def(x) and f(x)'
> would where def(x) is interpreted as a definedness predicate ?
>
> What "associativity" ?
>
> Does not 'def(x) and (x or y)' evaluate to the same as 'def(x) and x or
> def(x) and y' would where def(x) is interpreted as a definedness
> predicate ?
Date: Sun, 26 Aug 2007 10:12:25 +0200
Message-ID: <farcle$ars$1_at_orkan.itea.ntnu.no>
Quoth V.J. Kumar:
> Jan Hidders <hidders_at_gmail.com> wrote in
> news:1188037788.486939.308150_at_i38g2000prf.googlegroups.com:
>
>> On 25 aug, 02:13, "V.J. Kumar" <vjkm..._at_gmail.com> wrote: >>> 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 ?
>
> 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 ?
I believe the point is that if x is not defined, it makes no sense to evaluate f(x) (because we are using 2VL, and every expression /must/ have a value). In practical terms, you have to evaluate def(x) first, and only consider f(x) if def(x) is indeed TRUE. Contrast this with an ordinary AND expression, where it doesn't matter which term you evaluate first. Also, this makes it irrelevant what tautologies or contradictions may be present in f(x) when x is undefined---they are ignored regardless.
-- JonReceived on Sun Aug 26 2007 - 10:12:25 CEST