From @YaleVM.YCC.YALE.EDU:LOJBAN@CUVMB.BITNET Thu Feb 24 11:35:39 1994 Received: from ELI.CS.YALE.EDU by NEBULA.SYSTEMSZ.CS.YALE.EDU via SMTP; Thu, 24 Feb 1994 06:36:12 -0500 Received: from YALEVM.YCC.YALE.EDU by eli.CS.YALE.EDU via SMTP; Thu, 24 Feb 1994 06:36:08 -0500 Message-Id: <199402241136.AA01169@eli.CS.YALE.EDU> Received: from CUVMB.CC.COLUMBIA.EDU by YaleVM.YCC.Yale.Edu (IBM VM SMTP V2R2) with BSMTP id 7337; Thu, 24 Feb 94 06:34:37 EST Received: from CUVMB.COLUMBIA.EDU by CUVMB.CC.COLUMBIA.EDU (Mailer R2.07) with BSMTP id 7635; Thu, 24 Feb 94 06:35:08 EDT 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 To: lojban@cuvmb.cc.columbia.edu Status: RO X-Status: 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.