From jjllambias@hotmail.com Thu Aug 09 19:17:58 2001 Return-Path: X-Sender: jjllambias@hotmail.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-7_3_1); 10 Aug 2001 02:17:58 -0000 Received: (qmail 40836 invoked from network); 10 Aug 2001 02:17:57 -0000 Received: from unknown (10.1.10.27) by m8.onelist.org with QMQP; 10 Aug 2001 02:17:57 -0000 Received: from unknown (HELO hotmail.com) (216.33.241.92) by mta2 with SMTP; 10 Aug 2001 02:17:57 -0000 Received: from mail pickup service by hotmail.com with Microsoft SMTPSVC; Thu, 9 Aug 2001 19:17:57 -0700 Received: from 200.41.247.44 by lw8fd.law8.hotmail.msn.com with HTTP; Fri, 10 Aug 2001 02:17:57 GMT X-Originating-IP: [200.41.247.44] To: lojban@yahoogroups.com Bcc: Subject: Re: [lojban] A or B, depending on C, and related issues Date: Fri, 10 Aug 2001 02:17:57 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 10 Aug 2001 02:17:57.0636 (UTC) FILETIME=[ABC38440:01C12142] From: "Jorge Llambias" la pycyn cusku di'e > > [(if P then Q) and (if not P then R)] xor > > [(if not P then Q) and (if P then R)] > >Since this >all is out of the {makau} thread, which is about hiding significant >information, perhaps that is an important fact, but then we need to see how >these connections are going to work: (if Pkau then Q) and (if not-Pkau then >R)? No, Pkau is always true, so that one would reduce to (Q and R). >The best simplification I could find in a dash was ~(Q&R) &(P => QvR) , >which, while shorter, is markedly less informative when talking about >depndencies. Actually, that reduction fails when P, Q, and R are false. (It gives true, should give false.) The actual reduction, funnily enough, turns out to be (Q xor R), independent of P! What's more, this other one: [(P iff Q) and (not P iff R)] xor [(not P iff Q) and (P iff R)] also reduces to the same thing: (Q xor R). This makes sense, because the truth value of "Q or R depending on P" cannot depend on the truth value of P, since we are not specifying what the dependency is. This fits in very nicely with the Pkau interpretation, which might be: Pkau => (Q xor R) mu'o mi'e xorxes _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp