From pycyn@aol.com Fri Jun 23 09:10:04 2000 Return-Path: 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> Date: Fri, 23 Jun 2000 12:09:59 EDT Subject: RE:Trivalent logics To: lojban@egroups.com MIME-Version: 1.0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit X-Mailer: AOL 3.0 16-bit for Windows sub 41 From: pycyn@aol.com 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.