From sentto-44114-3204-961776603-mark=kli.org@returns.onelist.com Fri Jun 23 16:06:47 2000 Return-Path: Delivered-To: shoulson-kli@meson.org Received: (qmail 2189 invoked from network); 23 Jun 2000 16:06:46 -0000 Received: from zash.lupine.org (205.186.156.18) by pi.meson.org with SMTP; 23 Jun 2000 16:06:46 -0000 Received: (qmail 22331 invoked by uid 40001); 23 Jun 2000 16:10:10 -0000 Delivered-To: kli-mark@kli.org Received: (qmail 22328 invoked from network); 23 Jun 2000 16:10:10 -0000 Received: from mk.egroups.com (207.138.41.165) by zash.lupine.org with SMTP; 23 Jun 2000 16:10:10 -0000 X-eGroups-Return: sentto-44114-3204-961776603-mark=kli.org@returns.onelist.com Received: from [10.1.10.38] by mk.egroups.com with NNFMP; 23 Jun 2000 16:10:12 -0000 Received: (qmail 19339 invoked from network); 23 Jun 2000 16:10:02 -0000 Received: from unknown (10.1.10.142) by m4.onelist.org with QMQP; 23 Jun 2000 16:10:02 -0000 Received: from unknown (HELO imo-r20.mx.aol.com) (152.163.225.162) by mta3 with SMTP; 23 Jun 2000 16:10:02 -0000 Received: from Pycyn@aol.com by imo-r20.mx.aol.com (mail_out_v27.10.) id a.72.76c2cb (4405) for ; Fri, 23 Jun 2000 12:09:59 -0400 (EDT) Message-ID: <72.76c2cb.2684e5d7@aol.com> To: lojban@egroups.com X-Mailer: AOL 3.0 16-bit for Windows sub 41 From: pycyn@aol.com MIME-Version: 1.0 Mailing-List: list lojban@egroups.com; contact lojban-owner@egroups.com Delivered-To: mailing list lojban@egroups.com Precedence: bulk List-Unsubscribe: Date: Fri, 23 Jun 2000 12:09:59 EDT Subject: [lojban] RE:Trivalent logics Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit The formula I gave overestimates the number of distinct binary functions that can be defined with the formula given, since symmetric functions get defined twice at even the basic level (f1(x) + f2(y) and f2(x) + f1(y)). And some get defined even more times: the fixed value functions (always the same value whatever the input) can be worked off the corresponding unary fixed value function as any of f1, f2, f3, with the others being fixed 0. There are obviously other ways of doing these as well. The max function (greater value of x,y) can also be done in a variety of ways, including using functions that are 1 for 1, 0 otherwise as f1 and f2, -1 for 1 and 0 otherwise for f3. The three fixed functions and max, however, make a functionally complete system, one in which every three valued binary connective can be defined -- though often by very complex formula indeed. ------------------------------------------------------------------------ Get a NextCard Visa, in 30 seconds! 1. Fill in the brief application 2. Receive approval decision within 30 seconds 3. Get rates as low as 2.9% Intro or 9.9% Fixed APR http://click.egroups.com/1/5197/4/_/17627/_/961776603/ ------------------------------------------------------------------------ To unsubscribe, send mail to lojban-unsubscribe@onelist.com