From @uga.cc.uga.edu:lojban@cuvmb.bitnet Tue Jun 20 00:23:54 1995 Received: from punt2.demon.co.uk by stryx.demon.co.uk with SMTP id AA3463 ; Tue, 20 Jun 95 00:23:51 BST Received: from punt2.demon.co.uk via puntmail for ia@stryx.demon.co.uk; Mon, 19 Jun 95 10:05:19 GMT Received: from uga.cc.uga.edu by punt2.demon.co.uk id aa03149; 19 Jun 95 11:04 +0100 Received: from UGA.CC.UGA.EDU by uga.cc.uga.edu (IBM VM SMTP V2R2) with BSMTP id 1591; Mon, 19 Jun 95 05:59:26 EDT Received: from UGA.CC.UGA.EDU (NJE origin LISTSERV@UGA) by UGA.CC.UGA.EDU (LMail V1.2a/1.8a) with BSMTP id 3964; Mon, 19 Jun 1995 05:59:26 -0400 Date: Mon, 19 Jun 1995 02:53:06 -0700 Reply-To: Gerald Koenig Sender: Lojban list From: Gerald Koenig Subject: Re: pc answers X-To: lojban@cuvmb.cc.columbia.edu To: Iain Alexander Message-ID: <9506191104.aa03149@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). >> > jorge said: >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. djer adds: In (2.) it does not have to be the same man [singular] that does the touching. (2) states, "for some z1..." where z1 is clearly defined by pc to be the set {x,y,z} of three men. We have the existential quantifier E on z1. It is read as "for at least one..and less than all". It does not mean only one man. Here it can mean two men. Some {x,y,z}; or equivalently, E(z1) mean one only of the following list: [x,y,z,(x,y),(x,z),(y,z)]. This is a 6 member list. (2.) E(z1)(w1) t(z1,w1) means; select one member of the list, then pair it with each member of {u,v,w} (dog). Two men, for example (x,y), can touch each dog. E(w1) means one only of the list: [u,v,w,(u,v),(u,w),(v,w)]. This is the list for some dogs. The double existential form, E(z1)E(w1), requires a choice from each list to express the idea "some (of 3) men touch some (of 3) dogs." This yields 36 possibilities. I am not up to speed on default quantifiers, but if "su'o ci nanmu cu pencu su'o ci gerku" is the default then 36 different events are possible. The All-All double universal combination gives only one diagram, and either E-All or All-E each give 6 possible diagrams. What "ci nanmu cu pencu ci gerku" means can be narrowed down by explicit or default quantifiers; even then there is a bewildering array of possibilites except in the All-All case. And this is for the 3-3 case that pc provided to clarify the issues. Perhaps only the double universal case is useful, and beyond that we will have to describe what we mean or be content with the incomprehensibily of so much complexity. djer >All this still doesn't tell us what does {ci nanmu cu pencu ci gerku} >mean. > >Jorge >