On Tue, Jun 05, 2007 at 02:41:48PM +1000, Tony Morris wrote:
> I would like to know if all 16 possible functions that accept two
> boolean arguments have names in First-Order Logic. I know they have
> Haskell function names (e.g. \p -> \_ -> id p, \_ -> \_ -> const True),
> but I'm hoping there is a more general name that is recognised by anyone
> with a feel for logic, but not necessarily Haskell.
There are way more than 16, if you count partial and lazy functions.
> I have listed all sixteen of these functions below using Haskell (named
> a to p) along with the name of those that I am aware of having a name as
> a comment.
>
> Thanks for any tips.
>
> {-
>
> p q | a b c d e f g h i j k l m n o p
> 0 0 | 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
> 0 1 | 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
> 1 0 | 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
> 1 1 | 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
>
> -}
I see P/Q notation used a lot
> c :: Bool -> Bool -> Bool
> c False _ = False
> c _ q = not q
P∧¬Q
Also AND-NOT, commonly seen in electronics circles as it is the logic
function performed by a single transistor
Stefan
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