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Boolean Algebra (was: Re: Voiced Velar Fricative)

From: Dennis Paul Himes Friday, November 10, 2000, 4:47
```Steg Belsky <draqonfayir@...> wrote:
>
> On Wed, 8 Nov 2000 06:00:28 -0500 Carlos Thompson
> <carlos_thompson@...> writes:
> > > -Stephen (Steg)
> > >  "P i Q?  P oi Q?  P au Q?"
> >
> > Is this propositional algebra in Rokbeigalmki? (did I spell it
> > right?)
>
> Yup, you spelled it right!
> I'm not sure what propositional algebra is, but this is elementary logic:
It's usually known in English as propositional calculus, although that
has the disadvantage of potential confusion with differential and integral
calculus, which is what people mean when they say "calculus" with no
modifier.
It's also called 0-order logic, as opposed to first order logic, a.k.a.
prepositional calculus.  First order logic allows quantification over
objects, and second order logic allows quantification over sets of objects.

From: taliesin the storyteller <taliesin@...>
: * Steg Belsky <draqonfayir@...> [001109 02:36]:
: > (no symbol i know of) = au = "either-or" (in logic this is the negation
: > of "if-and-only-if", the biconditional)
:
: Exclusive-or, XOR:

With the other "or" known as inclusive or.

: an underlined \/, or in Boolean algebra, a plus in a circle.

I think it's the prevalence of the term "Boolean" in programming
languages which is responsible for the identification of Boolean algebra
with the propositional calculus.  This has grated on me somewhat in recent
years.  It's true that propositional calculus is a form of Boolean algebra,
but so are many other things.  I don't believe the plus in a circle is used
in general studies of Boolean algebras (although I could be wrong).  The
different forms of Boolean algebra, in fact, have several different
notations, such as:

General         +   *               -   0       1
Logic           v   &               ~   F       T
Set Theory      U   (upside down U) '   0       (universal set)
C bit maps      |   &               ~   0x0000  0xFFFF

The equivalent of exclusive or is known as symmetric difference in set
theory.
BTW: Boolean algebra is named after the English mathematician George
Boole (1815-1864).

===========================================================================

Dennis Paul Himes    <>    dennis@himes.connix.com
homepage: http://www.connix.com/~dennis/dennis.htm
Gladilatian page: http://www.connix.com/~dennis/glad/lang.htm

Disclaimer: "True, I talk of dreams; which are the children of an idle
brain, begot of nothing but vain fantasy; which is as thin of substance as
the air."                      - Romeo & Juliet, Act I Scene iv Verse 96-99
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