From @uga.cc.uga.edu:lojban@cuvmb.bitnet Tue Jun 27 22:30:20 1995 Received: from punt2.demon.co.uk by stryx.demon.co.uk with SMTP id AA3641 ; Tue, 27 Jun 95 22:30:17 BST Received: from punt2.demon.co.uk via puntmail for ia@stryx.demon.co.uk; Tue, 27 Jun 95 04:56:34 GMT Received: from uga.cc.uga.edu by punt2.demon.co.uk id aa23117; 27 Jun 95 5:55 +0100 Received: from UGA.CC.UGA.EDU by uga.cc.uga.edu (IBM VM SMTP V2R2) with BSMTP id 0955; Tue, 27 Jun 95 00:53:43 EDT Received: from UGA.CC.UGA.EDU (NJE origin LISTSERV@UGA) by UGA.CC.UGA.EDU (LMail V1.2a/1.8a) with BSMTP id 2892; Tue, 27 Jun 1995 00:53:34 -0400 Date: Mon, 26 Jun 1995 22:55:51 -0600 Reply-To: Chris Bogart Sender: Lojban list From: Chris Bogart Subject: proposed quant. scope cmavo: xu'u To: lojban@cuvmb.bitnet Message-ID: <9506270555.aa23117@punt2.demon.co.uk> Status: R I haven't been following this completely thoroughly, so it may be irrelevant or redundant. I especially agree with And that the whole matter of quantifier scope in afterthought form ought to be looked at all at once, rather than patched together piecemeal with new cmavo; but it's an interesting idea... --- It looks to me like the three/nine dog problem is that there's no way, even in the prenex, to indicate that two quantified variables exist at the same scope. That is, we can say (watch the "such that"s): "E3x, x is a man, SUCH THAT E3y, y is a dog, SUCH THAT x bites y" (i.e. there could be up to nine dogs) is IMO "ci nanmu cu batci ci gerku" or "ci nanmu ci gerku zo'u ny. gy. batci" But I don't know how to say: "E3x,3y, x is a man, y is a dog, SUCH THAT x bites y" (i.e. there are three men and three dogs, and each man bites each dog) in Lojban, since the two existential quantifiers are supposed to exist at the same level of scope (there's no "such that" between them) and I don't know a way of doing that either in the prenex or in afterthought. I hate to suggest this, being a general opponent of cmavo proliferation, but: If we have to add a cmavo, how about a "non-such-that" cmavo (what's left... xu'u?). Most of the time, you'd assume that between two existential quantifiers there was a "such that", getting the up-to-9-dog interpretation. But that could be overridden, in the prenex or the main sentence, by inserting xu'u before the second sumti: ci nanmu cu batci xu'u ci gerku or: ci nanmu xu'u ci gerku zo'u ny. batci gy. "xu'u" might be loosely glossed in Loglish as "the same", as in "Three men bit the same three dogs". I'm not sure what would happen if you tried to use this with nested things like "da poi ko'a nelci xu'u de". "xu'unai" might be a pedantic and always-elideable way of saying "such that"; it could be inserted between existentially quantified sumti in order to stress the up-to-nine-dog interpretation. [I wonder if there's some way of broadening the concept to fit such things as "respectively" as well... "ci nanmu cu batci ri" could be "three men bit themselves" and "ci nanmu cu batci xu'u ri" could be "three men each bit each other". I'm not sure if this makes sense or not, but there seems to be some similarity between the two problems...]