From jjllambias@hotmail.com Sun Jun 25 15:55:38 2000 Return-Path: Received: (qmail 8202 invoked from network); 25 Jun 2000 22:55:35 -0000 Received: from unknown (10.1.10.26) by m4.onelist.org with QMQP; 25 Jun 2000 22:55:35 -0000 Received: from unknown (HELO hotmail.com) (216.33.241.205) by mta1 with SMTP; 25 Jun 2000 22:55:35 -0000 Received: (qmail 4030 invoked by uid 0); 25 Jun 2000 22:55:35 -0000 Message-ID: <20000625225535.4029.qmail@hotmail.com> Received: from 200.32.23.248 by www.hotmail.com with HTTP; Sun, 25 Jun 2000 15:55:35 PDT X-Originating-IP: [200.32.23.248] To: lojban@egroups.com Subject: Re: [lojban] RE:Trivalent Logics Date: Sun, 25 Jun 2000 15:55:35 PDT Mime-Version: 1.0 Content-Type: text/plain; format=flowed From: "Jorge Llambias" Ok, this is what I propose for a trivalent system of unary operators in lojban: cai (1,-1,-1) sai (1,0,0) ru'e (1,1,-1) cu'i (0,1,-1) nai (-1,0,1) I think {cai}, {ru'e} and {nai} are the easiest to accept. (-1,0,1) is the most obvious generalization of {nai} from binary. (1,-1,-1) corresponds to the strongest assertion (certainty or necessity, depending on what system we use it on) so it has to be {cai}. (1,1,-1) is possibility or a weak assertion, so I think {ru'e} fits well. Now, (1,0,0) is also an assertion, but not as strong as certainty, something like "this is how it is, but I give no guarantees". I think {sai} can work for that. And finally, {cu'i} is for neutral. (0,1,-1) is not absolutely neutral, it is uncertainty with a bent towards assertion, but it is the closest to neutral and we do need it to generate others, so {cu'i} has to be it. With those 5 it is possible to generate all 27 unary functors, with at most three of them. For example, (0,0,1) is {naisai}, (-1,1,-1) is {cu'icai}, (0,0,0) is {sairu'ecu'i} (among several possibilities), etc. Only 8 of the 27 need three basic functions, the rest can be formed from just two. The nice thing about this system is that it can be used for different things. For example, for a strictly logical system we just attach them to {ja'a}, using {ja'acai}, {ja'acu'inai}, etc. And {na}={ja'anai}, so some of them can be shortened. But they can also be used for evidentials, attaching them to {ju'a} for example. Then again there might be some shortcuts, like {ju'acai} might be {za'a} and {ju'asairu'e} might be {ca'e}, etc, but we know that we can get all 27 of them from just the simplest, which is always (1,0,-1) and doesn't take any modifier. We can use {la'a} as the basis for the probabiliy set, etc. Would that work? co'o mi'e xorxes ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com