# Re: NULLs: theoretical problems?

Date: Sat, 11 Aug 2007 10:22:54 -0700

Message-ID: <1186852974.137534.280580_at_57g2000hsv.googlegroups.com>

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