Re: NULLs: theoretical problems?

From: V.J. Kumar <>
Date: Mon, 27 Aug 2007 14:30:26 -0700
Message-ID: <>

Jan Hidders wrote:
> On 27 aug, 01:46, "V.J. Kumar" <> 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 ?

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.


> -- Jan hidders
Received on Mon Aug 27 2007 - 23:30:26 CEST

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