Return-Path: <@FINHUTC.HUT.FI:LOJBAN@CUVMB.BITNET> Received: from FINHUTC.hut.fi by xiron.pc.helsinki.fi with smtp (Linux Smail3.1.28.1 #14) id m0pZeN4-0000PfC; Thu, 24 Feb 94 13:36 EET Message-Id: Received: from FINHUTC.HUT.FI by FINHUTC.hut.fi (IBM VM SMTP V2R2) with BSMTP id 6655; Thu, 24 Feb 94 13:36:32 EET Received: from SEARN.SUNET.SE (NJE origin MAILER@SEARN) by FINHUTC.HUT.FI (LMail V1.1d/1.7f) with BSMTP id 6651; Thu, 24 Feb 1994 13:36:32 +0200 Received: from SEARN.SUNET.SE (NJE origin LISTSERV@SEARN) by SEARN.SUNET.SE (LMail V1.2a/1.8a) with BSMTP id 3087; Thu, 24 Feb 1994 12:35:33 +0100 Date: Thu, 24 Feb 1994 11:35:39 GMT Reply-To: i.alexander.bra0125@oasis.icl.co.uk Sender: Lojban list From: i.alexander.bra0125@OASIS.ICL.CO.UK Subject: Re: TECH: Quantifiers; Confusing prenexes X-To: lojban@cuvmb.cc.columbia.edu To: Veijo Vilva Content-Length: 2595 Lines: 65 la lojbab. cusku di'e > Does this help??? Yes, it does - to clarify the issues if nothing else. > (1b) {de zo'u [ro da poi (da) broda de vau] [ro de poi brode da]} zo'u ... This highlights one of the problems I have. I'm used to logical systems where the second quantification of {de}, the {ro de li'o}, introduces a new {de} with a nested (or at least different) scope. We even have a rule somewhere that says that a new quantification of a previously- used variable name introduces a new variable with its own scope. (Let's call this rule R.) Is this what's going on here? If not, it is somehow the same {de} as before, but we are subselecting only those such that {de brode da}. This looks to me like it is an abbreviation for an expression introducing a new variable (name) {di}, something like ro di po'u de zi'e poi brode da or, perhaps even clearer, a preliminary clause in the body of the jufra, such as li'o zo'u de brode da .inaja li'o This is the case which has been causing problems in interpretation. If zu'unai the new quantification introduces a completely new variable, then everything's much simpler. But I don't see what makes this any better-formed than (1a): > (1a) [ro da poi {de zo'u (da) broda de vau}] [ro de poi brode da] zo'u ... Both have a {de} in the {ro da li'o} section, and then a new {de} introduced by the following quantification. It would be clearer with a new variable name {di}, but I don't see any fundamental problem. In fact, this would be the natural and default interpretation of (1) [ro da poi broda de vau] [ro de poi brode da] zo'u ... ta'o Is there any difference between { zo'u} and { zo'u zo'u}? There doesn't seem to be any reason why there should be. ta'onai > Nora says that if you want in any way to have the variable subordinate > to "de" to be quantified any OTHER way than under the "roda" scope > previously expressed, it also must be expressed as a separate variable, > newly quantified (presumably) within the subordinate clause prenex. At first I couldn't make any sense of this at all. Now I think you must mean 'the variable subordinate to "de"' to mean the {da} in the {[ro de poi brode da]} in (1a), in which case I understand. But I'm not sure I agree. If there were an explicit quantifier (e.g. {su'o}), I don't see why rule (R) shouldn't apply to give a new variable. The first part of the prenex would become totally redundant, since both its variable names have just become redefined, but the end result is well-defined and meaningful. mu'o mi'e .i,n.