Re: [lojban] polyadic connectives

[Robin Lee Powell <rlpowell@digitalkingdom.org>]

On Sat, Aug 18, 2001 at 07:22:13AM +0100, And Rosta wrote:
> Robin:
> > On Sat, Aug 18, 2001 at 04:22:09AM +0100, And Rosta wrote:
> > > There was some recent discussion, instigated by pc, about
> > > more-than-binary connectives. For some, like an extended xor, it's
> > > easy to see how to render them: "exactly one of A, B, C is true". 
> > 
> > Umm, no.
> > 
> > IIRC, this is even mentioned in the book as an example of one that
> > doesn't work.  Here's the table, assuming left associativity:
> > 
> > A       xor     B       Result  C
> > T       F       T       T       T
> > T       F       T       F       F
> > T       T       F       F       T
> > T       T       F       T       F
> > F       T       T       F       T
> > F       T       T       T       F
> > F       F       F       T       T
> > F       F       F       F       F
> > 
> > IOW, it's true when exactly one is true and when all are true.  Rather
> > counter-intuitive.
> 
> In this case it doesn't mean "exactly one of A, B, C is true", which
> is an extension of "exactly one of A, B is true", which is one way of
> doing xor. I can't easily work out what your table means, but I
> imagine it's xor(A, xor(B, C)) or suchlike,

Well, yes, it was.

Is there another way to commute XOR that I'm unaware of?

If you're going to treat A xor B xor C as something other than one of:

(A xor B) xor C
A xor (B xor C)

then you've got an operator that's not xor anymore.

-Robin

-- 
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