# Re: NULLs: theoretical problems?

From: Cimode <cimode_at_hotmail.com>
Date: Sat, 11 Aug 2007 10:22:54 -0700

On 11 août, 16:14, Jan Hidders <hidd..._at_gmail.com> wrote:
> On Aug 11, 3:59 am, Aloha Kakuikanu <aloha.kakuik..._at_yahoo.com> wrote:
>
>
>
> > On Aug 10, 4:52 pm, "V.J. Kumar" <vjkm..._at_gmail.com> wrote:
>
> > > "David Portas" <REMOVE_BEFORE_REPLYING_dpor..._at_acm.org> wrote innews:NM-dncYFOuhqBybb4p2dnAA_at_giganews.com:
>
> > > > "paul c" <toledobythe..._at_oohay.ac> wrote in message
> > > >news:JXLui.45171\$rX4.26997_at_pd7urf2no...
>
> > > >> (even though I'm not sure in "s{X} = t{X} implies s{Y} = t{Y}"
> > > >> whether "implies" stands for logical implication.)
>
> > > > Good catch. It seems that logical implication is not well defined for
> > > > three-value logic.
>
> > > It is not that three-valued implication is not 'well defined' whatever it
> > > means. As a matter of fact, there are a few competing definitions to
> > > choose from, Lukaciewicz's, Kleene's and someone else's whose name I do
> > > not recall. They define implication in the usual way, with the truth
> > > table.
>
> > I wonder if 3-rd value logic interpretation is trivial. Take any
> > boolean algebra that is more than 2 valued, and partition its elements
> > into 3 equivalence classes. For example, one may define True as
> > maximal element, False as a minimal one, and combine all the rest into
> > Unknown. For four element BA we have:
>
> > 00 -- False
> > 01 -- Unknown
> > 10 -- Unknown
> > 11 -- True
>
> > Sure in this model formal implication "Unknown -> Unknown" evaluates
> > to True or Unknown:
>
> > "01 -> 01" = "01 \/ ~01" = "01 \/ 10" = "11" -- true
>
> > on the other hand
>
> > "01 -> 10" = "01 \/ ~10" = "01 \/ 01" = "01" -- unknown
>
> > So the problem is to make the partition of BA elements to respect BA
> > operations, so that the later can be defined consistently. Apparently,
> > one can have consistent 4 valued logic, but not 3 valued one. Am I
> > missing anything?
>
> Yes. The problem is not that there is no consistent interpretation but
> that there is more than one. Apart form the fact that with a truth
> table approach you will always have the problem that (P \/ ~P) will
> never evalutate to TRUE if P is not TRUE or FALSE. But that is of
> course the usual trade off between "what we really want" and "what can
> be efficiently computed".
Multiplication of theories is a consequence of subjective and anthropomorphic characterization of database management. I liked a debunked article once coming that exposed a new interpretation based on 128 types of NULLS. The issue was precisely on that matter.
> -- Jan Hidders
Received on Sat Aug 11 2007 - 19:22:54 CEST

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