From @uga.cc.uga.edu:lojban@cuvmb.bitnet Sun Jun 18 00:05:42 1995 Received: from punt2.demon.co.uk by stryx.demon.co.uk with SMTP id AA3456 ; Sun, 18 Jun 95 00:05:41 BST Received: from punt2.demon.co.uk via puntmail for ia@stryx.demon.co.uk; Sun, 18 Jun 95 15:57:01 GMT Received: from uga.cc.uga.edu by punt2.demon.co.uk id aa17358; 18 Jun 95 16:56 +0100 Received: from UGA.CC.UGA.EDU by uga.cc.uga.edu (IBM VM SMTP V2R2) with BSMTP id 0747; Sun, 18 Jun 95 11:54:19 EDT Received: from UGA.CC.UGA.EDU (NJE origin LISTSERV@UGA) by UGA.CC.UGA.EDU (LMail V1.2a/1.8a) with BSMTP id 9098; Sun, 18 Jun 1995 11:54:19 -0400 Date: Sun, 18 Jun 1995 10:46:48 EDT Reply-To: jorge@phyast.pitt.edu Sender: Lojban list From: jorge@phyast.pitt.edu Subject: Re: pc answers X-To: lojban@cuvmb.cc.columbia.edu To: Iain Alexander Message-ID: <9506181656.aa17358@punt2.demon.co.uk> Status: R la djer cusku di'e > 1. (z1)(w1) t(z1,w1). For each z1, For each w1, touches( z1,w1). > 2. E(z1)(w1) t(z1,w1). For some z1, For each w1, touches(z1, w1). > 3. E(w1)(z1) t(z1,w1). etc. > 4. (z1)E(w1) t(z1,w1). > 5. (w1)E(z1) t(z1,w1). > 6. E(z1)E(w1)t(z1,w1). > > As I understand it the order here in the prenex does not matter; so > 2. is equivalent to 5; and 3. is equivalent to 4. Actually, the order does matter. 2. says that there is at least one man, such that he touches each of the three dogs. 5. says that each of the three dogs is touched by at least one man. In 2., it has to be the same man that does the touching, while in 5. it can be a different one for each dog. > This yields only 4 distinct forms. > > This is reasonable because the form p[Q{w1}, Q{z1}] where p is a > predicate and Q a quantifier (either the universal or the existential), > has exactly 4 permutations. It has 8 permutations (two possibilities for each Q, times two possible orders of the arguments, 2^3=8). But since (z1)(w1) is equivalent to (w1)(z1), and E(z1)E(w1) is the same as E(w1)E(z1) there are left only six that are different. The order of universal and existential quantifier matters. The order of two universals or two existentials doesn't. All this still doesn't tell us what does {ci nanmu cu pencu ci gerku} mean. Jorge