Reply-To: <a.rosta@ntlworld.com>
To: "Robin Lee Powell" <rlpowell@digitalkingdom.org>,
	"Lojban@Yahoogroups. Com" <lojban@yahoogroups.com>
Subject: RE: [lojban] polyadic connectives
Date: Sat, 18 Aug 2001 07:22:13 +0100
Message-ID: <LPBBJKMNINKHACNDIIGMKEHBEJAA.a.rosta@dtn.ntl.com>
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From: "And Rosta" <a.rosta@dtn.ntl.com>
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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, which would not count as 
the sort of connective I was rather incompetently trying to describe.

--And.