From a.rosta@ntlworld.com Fri Aug 17 20:25:20 2001 Return-Path: X-Sender: a.rosta@ntlworld.com X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-7_3_1); 18 Aug 2001 03:25:20 -0000 Received: (qmail 50525 invoked from network); 18 Aug 2001 03:25:20 -0000 Received: from unknown (10.1.10.26) by l10.egroups.com with QMQP; 18 Aug 2001 03:25:20 -0000 Received: from unknown (HELO mta02-svc.ntlworld.com) (62.253.162.42) by mta1 with SMTP; 18 Aug 2001 03:25:19 -0000 Received: from andrew ([62.255.40.23]) by mta02-svc.ntlworld.com (InterMail vM.4.01.03.00 201-229-121) with SMTP id <20010818032518.KGLD29790.mta02-svc.ntlworld.com@andrew> for ; Sat, 18 Aug 2001 04:25:18 +0100 To: "Lojban@Yahoogroups. Com" Subject: polyadic connectives Date: Sat, 18 Aug 2001 04:22:09 +0100 Message-ID: MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 (Normal) X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook IMO, Build 9.0.2416 (9.0.2910.0) Importance: Normal X-MimeOLE: Produced By Microsoft MimeOLE V5.00.2615.200 From: "And Rosta" X-Yahoo-Message-Num: 9735 There was some recent discussion, instigated by pc, about more-than-binary connectives. For some, like an extended xor, it's easy to see how to render them: "exactly one of A, B, C is true". I've got two questions: 1. What connectives make sense when extended to sets of varying size? (What's the term for what I mean? Commutative functions? Ones where all arguments are treated alike.) * and = all of * or = at least one of * extended xor = exactly one of * extended iff = all of or none of * ... and what else? (apart from negations of these four) 2. Does Lojban have any way of doing "all or none" without resorting to an explicit disjunction? For example, is there a way of saying "more than none and less than all", without the conjunction? --And.