Print

Print


On 3/16/06, Patrick Littell <[log in to unmask]> wrote:

> You can make do with just IF and NOT; Lukasiewicz's axiomatization of
> sentential logic has these as the primitives, iirc.
>
> A OR B = IF NOT A THEN B
> A AND B = NOT ( IF A THEN NOT B )
>

Looked it up: although Lukasiewicz's axioms only make use of IF and
NOT, it looks like he actually chose IF and AND as the primitives, and
then defined IF as NOT ( A AND NOT B).  I found his axioms, too:

1.  ( P => Q ) => ( ( Q => R ) => ( P => R ) )
2.  P => ( ~ P => Q )
3.  ( ~ P => P ) => P

It's amazing that we can get the entirety of sentential logic from
just these three.  (For some value of amazing.)  If you were to make
up native speakers for your minimally conjoining language, these
should be their Commandments.

I got this from John Halleck's great page at
http://home.utah.edu/~nahaj/logic/structures/index.html

-- Pat