From jjllambias@hotmail.com Sat Jun 24 17:08:48 2000 Return-Path: Received: (qmail 4027 invoked from network); 25 Jun 2000 00:08:46 -0000 Received: from unknown (10.1.10.26) by m1.onelist.org with QMQP; 25 Jun 2000 00:08:46 -0000 Received: from unknown (HELO hotmail.com) (216.33.240.206) by mta1 with SMTP; 25 Jun 2000 00:08:46 -0000 Received: (qmail 27041 invoked by uid 0); 25 Jun 2000 00:08:46 -0000 Message-ID: <20000625000846.27040.qmail@hotmail.com> Received: from 200.32.23.232 by www.hotmail.com with HTTP; Sat, 24 Jun 2000 17:08:46 PDT X-Originating-IP: [200.32.23.232] To: lojban@egroups.com Subject: Re: [lojban] RE:Trivalent Logics Date: Sat, 24 Jun 2000 17:08:46 PDT Mime-Version: 1.0 Content-Type: text/plain; format=flowed From: "Jorge Llambias" la pycyn cusku di'e >Ooops! For functional completeness the system needs min(x,y), too and that >seems harder to get. Once it is gotten, however, it alone generates all of >the connectives (binary, unary, more-ary), or rather the Sheffer function, >min(x,y)+1, does. Is there a simple :) way to see that this is true? It seems to me that max(x,y) is the most useful "or", and min(x,y) is the most useful "and", so it is nice that they are relatively straightforward to generate. >I think (disclaimer) that min can be defined with f1=f2 :-1 for -1, 0 >otherwise and f3 as 1for 1, 0 otherwise. But my head is not functioning >well >in -1,0,1 arithmetic at the moment. It does indeed give the minimum. So this is really the same situation we have in Lojban with respect to 3-way connectives, right? They can all be generated but not without repeating some of the arguments in some cases. Now the question is, do we have anything like a complete three-value unary system in Lojban? Obviously not a logic system (we only have na and ja'a there) but maybe with some set of attitudinals? {ju'a} or {je'u} (1,0,-1) {ju'o} (1,-1,-1) {la'a} (1,0,0) {ca'e} or {se'o} or {ai} (1,1,1) {pe'i} (0,0,0) ?? Could we produce some coherent system out of what we have? co'o mi'e xorxes ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com