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

"Peter Koch Larsen" <pkl_at_mailme.dk> wrote in message news:<3ea90ba0$0$42548$edfadb0f_at_dread11.news.tele.dk>...
> "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.

Firstly:
Commutative Laws, Distributive Laws, Identity Laws, Complement Laws

Check any text on the subject for details.

Secondly:
This is not an extension to boolean algebra. Think of it like talking about chairs in one case (boolean) and grasshoppers in the other. The only allowable entension to 2VL (Boolean) that you can logically have is to increase the number of elements as an integer power of 2.

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

you can also have

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

This is just as valid as the choice you made so which is correct. A similar thing can occur with * and ~. Many years ago now I looked at ternary based computing systems and finally realized that you could not do boolean logic with them. A completely different system would have to be developed.
>
> > * 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

Peter,

I don't know what you background is but I would seriously suggest that you get some engineering texts on switching theory, logic design and try to understand the fundementals. Then look at predicate theory as the next step.

Because it is "so easy" these days to "program", that those getting into it are not being encouraged to learn some of the fundementals. Compare with say car mechanics, it is possible to learn how to fix a car by doing it as a hobby but I know that for myself I get the best trained mechanic to work on my car - because he knows all the fundemantals as well as the rest. By the way, my mechanic is the best I ever seen and I travel to the next town to get to him.

What I'm saying is that it's easy these days to get some program working but is it doing the job as it is supposed to and is it doing it properly. The same with databases etc.

-- 
Bruce Rennie ( from God's Own Country Downunder )
Disciple of Jesus Christ in Training

The Cross of Jesus Christ - Salvation for all men.

Song of Solomon ( Song of Songs ) - The greatest Love Story Ever
and a story for our times.

Be a GOD Chaser.