From pycyn@aol.com Thu Jan 31 15:07:29 2002 Return-Path: X-Sender: Pycyn@aol.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_0_1_3); 31 Jan 2002 23:07:29 -0000 Received: (qmail 82332 invoked from network); 31 Jan 2002 23:07:29 -0000 Received: from unknown (216.115.97.171) by m5.grp.snv.yahoo.com with QMQP; 31 Jan 2002 23:07:29 -0000 Received: from unknown (HELO imo-r06.mx.aol.com) (152.163.225.102) by mta3.grp.snv.yahoo.com with SMTP; 31 Jan 2002 23:07:29 -0000 Received: from Pycyn@aol.com by imo-r06.mx.aol.com (mail_out_v31_r1.26.) id r.183.2f29e68 (4541) for ; Thu, 31 Jan 2002 18:07:25 -0500 (EST) Message-ID: <183.2f29e68.298b282c@aol.com> Date: Thu, 31 Jan 2002 18:07:24 EST Subject: Re: UI for 'possible' (was: Re: [lojban] Bible translation style question) To: lojban@yahoogroups.com MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="part1_183.2f29e68.298b282c_boundary" X-Mailer: AOL 7.0 for Windows US sub 118 From: pycyn@aol.com X-Yahoo-Group-Post: member; u=2455001 X-Yahoo-Profile: kaliputra X-Yahoo-Message-Num: 13138 --part1_183.2f29e68.298b282c_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit In a message dated 1/30/2002 8:33:35 PM Central Standard Time, jjllambias@hotmail.com writes: > The system was: > > cai (1,-1,-1) > sai (1,0,0) > ru'e (1,1,-1) > cu'i (0,1,-1) > nai (-1,0,1) > > and the operator (0,1,-1) is essential in order to be able > to have a complete system. You need either that one or (-1,1,0). > Strictly, the requirements for the smallest complete set are that there be on rotation (not used here, since it is derivable with extra functions -- (-1,1,0) or (0,-1,1)), one exchange (here (0,1-1), exchanging the first and second places) and one identification (the first three above). These three give the whole system and do so in a normative way (identifications at beginning and end, rearrangements only in between). This pattern works for any finite number of truth values from 2 up, with the peculiarity that for 2, the rotation and exhange are the same: negation. --part1_183.2f29e68.298b282c_boundary Content-Type: text/html; charset="US-ASCII" Content-Transfer-Encoding: 7bit



In a message dated 1/30/2002 8:33:35 PM Central Standard Time, jjllambias@hotmail.com writes:


The system was:

cai (1,-1,-1)
sai (1,0,0)
ru'e (1,1,-1)
cu'i (0,1,-1)
nai (-1,0,1)

and the operator (0,1,-1) is essential in order to be able
to have a complete system. You need either that one or (-1,1,0).


Strictly, the requirements for the smallest complete set are that there be on rotation (not used here, since it is derivable with extra functions -- (-1,1,0) or (0,-1,1)), one exchange (here (0,1-1), exchanging the first and second places) and one identification (the first three above).  These three give the whole system and do so in a normative way (identifications at beginning and end, rearrangements only in between).  This pattern works for any finite number of truth values from 2 up, with the peculiarity that for 2, the rotation and exhange are the same: negation. --part1_183.2f29e68.298b282c_boundary--