Exotic Logics

[Aaron Brady]

On Jun 17, 1:28 am, Steven D'Aprano
<ste... at REMOVE.THIS.cybersource.com.au> wrote:
> On Tue, 16 Jun 2009 22:46:14 -0700, William Clifford wrote:
> > I was staring at a logic table the other day, and I asked myself, "what
> > if one wanted to play with exotic logics; how might one do it?"
>
> First question: what's an exotic logics?
>
> Do you mean things like three-value logic, fuzzy logic, probabilistic
> reasoning, etc?

You (OP) may be interested in the definitions of the fuzzy operators:

and( x, y ) := min( x, y )
or( x, y ) := max( x, y )
not( x ) := 1 (one)- x
nand( x, y ) := not( and( x, y ) ) = 1- min( x, y )

Defining 'xor' as '( x or y ) and ( not( x and y ) )', we have:

xor( x, y ) := min( max( x, y ), 1- min( x, y ) )

However, defining 'xor' as '( x and not y ) or ( y and not x )', we
don't have:

xor( x, y ) := max( min( x, 1- y ), min( y, 1-x ) )

Good question.