Re: NULLs: theoretical problems?

On Aug 27, 10:30 pm, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
> Jan Hidders wrote:
> > On 27 aug, 01:46, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
> > > It should be blindingly obvious that I meant your DEF logic. I'll say
> > > it again: does not 'def(x) and f(x)'' commute in your logic if def(x)
> > > is understood as a definedness predicate and if the answer is "no",
> > > why it doesn't commute ?
>
> > Because the result of applying commutativity and associativity rules
> > to a formula that is allowed might be a formula that is not allowed.
> > For example, 'def(x) : x and y' might be rewritten to 'x and (def(x) :
> > y)'.
>
> Ok, I see your point. Technically, in the def logic , 'x or true' is
> undefined if x is undefined because you did not provide a line in the
> OR truth table for this case. Does it sound right ? Had you provided
> the line, then def(x) interpretation as a predicate wouldn't be a
> problem, commutativity etc. would work as it does in the classical
> logic and the logical formulae evaluation would have same as it is
> with 'def(x)' construct, and expressivity would probably be the same
> too unless I am missing something again.
>
> A natural question arises what is the def construct ? Is it a
> classical logic extension ?

PMFJI but I'm struggling to see why you believe there is a diversion from classical logic. How does def differ in your mind from the existential quantifier?

I am also unclear why one would ever favour 3VL in general. When I ask for a subset from a set of propositions (via a select clause say), well, I need a DBMS to be able to fulfill that request. I can't ever imagine a situation where I'd want the system to be "unsure" of what goes into that subset. Surely by encoding accurately, not using metadata, etc that situation need never arise - isn't that instinctively more desirable?

>
> The above is a mere technicality of course. What really bothers me is
> the fact that I really do not see much gain in comparison to using the
> three valued SQL logic. In addition to the de facto loss of the 'x
> or not x' tautology when x is undefined and we are forced to have the
> 'def(x) :(x or not x)' which evaluates to 'false' , we also lose
> the 'x or true' tautology for undefined x. While we can put forward
> some explanation for the former as Lukasiewicz and friends did, I do
> not see any intuition for the latter. 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. Please comment.

I personally don't see where the tautology is lost. For example:

Ex ( (P(x) AND f(x)) OR ¬(P(x) AND f(x) )

is always true, as is the general case. But obviously the following is not always true:

Ex ( (P(x) AND (f(x) OR ¬f(x)))

because P might not apply at all to the item under consideration. e.g. an equivalent question might be to ask whether a topology is a euclidian or non-euclidian space? The answer would be neither, because a topology isn't a geometrical space at all.

Regards, Jim
(suitably impressed that your posting from your phone.)

>
>
>
> > -- Jan hidders
Received on Tue Aug 28 2007 - 03:20:13 CEST