From rlpowell@digitalkingdom.org Fri Aug 17 23:28:38 2001 Return-Path: X-Sender: rlpowell@digitalkingdom.org X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-7_3_1); 18 Aug 2001 06:28:38 -0000 Received: (qmail 42023 invoked from network); 18 Aug 2001 06:28:37 -0000 Received: from unknown (10.1.10.26) by l8.egroups.com with QMQP; 18 Aug 2001 06:28:37 -0000 Received: from unknown (HELO chain.digitalkingdom.org) (64.169.75.101) by mta1 with SMTP; 18 Aug 2001 06:28:37 -0000 Received: from rlpowell by chain.digitalkingdom.org with local (Exim 3.32 #1 (Debian)) id 15Xzb2-0000TV-00 for ; Fri, 17 Aug 2001 23:28:36 -0700 Date: Fri, 17 Aug 2001 23:28:36 -0700 To: "Lojban@Yahoogroups. Com" Subject: Re: [lojban] polyadic connectives Message-ID: <20010817232835.F15595@digitalkingdom.org> Mail-Followup-To: "Lojban@Yahoogroups. Com" References: <20010817203321.A15595@digitalkingdom.org> Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Disposition: inline In-Reply-To: User-Agent: Mutt/1.3.20i From: Robin Lee Powell 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 -- http://www.digitalkingdom.org/~rlpowell/ BTW, I'm male, honest. le datni cu djica le nu zifre .iku'i .oi le so'e datni cu to'e te pilno je xlali -- RLP http://www.lojban.org/