Reply-To: <a.rosta@ntlworld.com>
To: "Lojban@Yahoogroups. Com" <lojban@yahoogroups.com>
Subject: RE: [lojban] polyadic connectives
Date: Sat, 18 Aug 2001 15:24:12 +0100
Message-ID: <LPBBJKMNINKHACNDIIGMOEHHEJAA.a.rosta@dtn.ntl.com>
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From: "And Rosta" <a.rosta@dtn.ntl.com>
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Robin:
> > 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.

By "extended xor" I didn't mean "iterated binary xor" (i,e, xor
with another xor as an argument), I meant "xor extended so that 
it has any number of arguments". If you analyse binary xor as 
"exactly one of the set {p, q}", then this can easily be extended 
to "exactly one of the set {p, q, r, s, t, ...}".

It seems to me that all of the nonbinary connectives we are likely
to want to use -- or to be intellectually up to using -- are of this
sort. Counterexamples are welcome.

--And.