From jjllambias@hotmail.com Sun Jun 18 16:15:53 2000 Return-Path: Received: (qmail 3141 invoked from network); 18 Jun 2000 23:15:51 -0000 Received: from unknown (10.1.10.27) by m3.onelist.org with QMQP; 18 Jun 2000 23:15:51 -0000 Received: from unknown (HELO hotmail.com) (216.33.240.175) by mta2 with SMTP; 18 Jun 2000 23:15:51 -0000 Received: (qmail 67406 invoked by uid 0); 18 Jun 2000 23:15:51 -0000 Message-ID: <20000618231551.67405.qmail@hotmail.com> Received: from 200.42.152.130 by www.hotmail.com with HTTP; Sun, 18 Jun 2000 16:15:51 PDT X-Originating-IP: [200.42.152.130] To: lojban@egroups.com Subject: Re: [lojban] Trivalent logic [was: Re: the logical language] Date: Sun, 18 Jun 2000 16:15:51 PDT Mime-Version: 1.0 Content-Type: text/plain; format=flowed From: "Jorge Llambias" la robin cusku di'e >Jorge's Aymara link reminded me of a question that had been turning over >in my mind of late; namely, is there any expression in trivalent, >multivalent or fuzzy logic which cannot be rephrased in "normal" >bivalent logic? Well, yes and no... :) I'm not sure whether the question makes sense. An expression is not really phrased in any logic. You take the same expression and depending on what logic you're using you can assign it a truth value. >For example, let's say we give the statement "Foobars like to be >globbed" a truth value of 0.8 . If you were using bivalent logic you could not do that. You could only give it a value of true or false. What you are doing is evaluating the statement using fuzzy logic, and then transforming it into other statements: >I would interpret this as either > "80% of foobars like to be globbed" >or > "There is 80% certainty that all foobars like to be globbed" >or > "A typical foobar, if asked to express its liking for being globbed on >a scale from 0 to 1, would give an answer of 0.8" >or some combination of these, all of which are simple true/false >statements. Or not. They are just statements, which you can evaluate using true/false logic, or using other logics. There is nothing that makes these statements more or less bivalent than the original one. Maybe they are more precise statements, but equally subject to any valued logic. I think what is interesting about Aymara is that apparently (from what I can tell from that paper) it is very easy to make trivalent logical operations. Lojban is not designed for that. In bivalent logic there are 4 possible unary operations: affirmation, negation, tautology and contradiction. Given a value of true, affirmation gives true, negation gives false, tautology gives true and contradiction gives false. For a value of false, affirmation gives false, negation gives true, tautology gives true and contradiction gives false. In Lojban two of these unary operations are represented: affirmation (ja'a) and negation (na). The other two are not so useful and there is no cmavo of selmaho NA that makes any sentence true, or one that makes any sentence false. A trivalent logic, instead of these four unary operators has 27 possible operators, and Aymara uses suffixes on the verb to represent them. These can be compounded so that only 9 suffixes are enough to cover all the operations, just like {nana} really could be used instead of {ja'a} in bivalent logic. This does not mean that you cannot use trivalent logic in Lojban. All it means is that the trivalent operations are not immediately transparent the way the bivalent ones are. And of course, for bivalent logic the interesting stuff only shows up in binary operations (the connectives) whereas in a trivalent logic the unary operations already have lots of interesting things (necessary, probable, possible, impossible, etc, are some of the things that Aymara handles this way). co'o mi'e xorxes ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com