Return-Path: <@SEGATE.SUNET.SE:LOJBAN@CUVMB.BITNET> Received: from SEGATE.SUNET.SE by xiron.pc.helsinki.fi with smtp (Linux Smail3.1.28.1 #1) id m0sQShZ-0000YjC; Tue, 27 Jun 95 07:56 EET DST Message-Id: Received: from segate.sunet.se by SEGATE.SUNET.SE (LSMTP for OpenVMS v0.1a) with SMTP id 780C7827 ; Tue, 27 Jun 1995 6:55:36 +0200 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 X-To: lojban@cuvmb.bitnet To: Veijo Vilva Content-Length: 2379 Lines: 53 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...]