Re: The BOOLEAN data type - What is really Boolean and what is not?

"Damjan S. Vujnovic" <damjan_at_galeb.etf.bg.ac.yu> skrev i en meddelelse news:b85ldc$h0c$1_at_news.etf.bg.ac.yu...
> > > Since three valued logic is not Boolean ( there are a number of
> > > different ways the logic operations can be written ( for 3VL-AND and
> > > 3VL-OR and 3VL-NOT )), you have to decide on the particular operations
> > > that you will allow and how the results will be calculated. Therefore,
> > > the normal Boolean operations of AND and OR and NOT cannot and do not
> > > work with three value domains.
> >
> > I am not sure I understand you.
>
> You cannot define operators AND and OR on a 3-element set in such a way
that
> all axioms of Boolean algebra are satisfied. Try to fill-out those two
> tables in such a way that axioms hold:

With the risk of sounding very uneducated let me ask which axioms you are referring to. Also, I would like to ask why such axioms should hold considering we are not discussing boolean algebra but an extension to it. I would be happy if only all axioms would hold whenever no nulls were involved.

>
> + T F N
> T ? ? ?
> F ? ? ?
> N ? ? ?
>

+ T F N
T T T T
F T F N
N T N F

> * T F N
> T ? ? ?
> F ? ? ?
> N ? ? ?
>

• T F N T T F N F F F F N N F N

~ T F N

   F T N
>
> T=True F=False N=Null(or whatever) +=OR *=AND
~= "NOT"
>

Very naive, perhaps ;-)

> Hint: The problem will be the existence of the inverse element...
Give me a little more help, please.

Kind regards
Peter Koch Larsen Received on Fri Apr 25 2003 - 12:19:12 CEST