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 m0pWSYz-0000PgC; Tue, 15 Feb 94 18:23 EET Message-Id: Received: from FINHUTC.HUT.FI by FINHUTC.hut.fi (IBM VM SMTP V2R2) with BSMTP id 0579; Tue, 15 Feb 94 18:18:48 EET Received: from SEARN.SUNET.SE (NJE origin MAILER@SEARN) by FINHUTC.HUT.FI (LMail V1.1d/1.7f) with BSMTP id 0577; Tue, 15 Feb 1994 18:18:46 +0200 Received: from SEARN.SUNET.SE (NJE origin LISTSERV@SEARN) by SEARN.SUNET.SE (LMail V1.2a/1.8a) with BSMTP id 6432; Tue, 15 Feb 1994 17:17:36 +0100 Date: Tue, 15 Feb 1994 10:49:59 -0500 Reply-To: Logical Language Group Sender: Lojban list From: Logical Language Group Subject: Re: TECH: Quantifiers (was: cukta) X-To: lojban@cuvmb.cc.columbia.edu To: Veijo Vilva In-Reply-To: <9402151311.AA26953@getafix.oasis.icl.co.uk> from Content-Length: 2339 Lines: 53 mi pu cusku di'e > > The scope of a quantified variable extends from: > > > the most recent place where a "prenex" grammatical construct > > could have occurred, viz. the innermost relative clause, > > abstraction, GEK-GIK-connected subsentence, main sentence, > > TUhE-TUhU supersentence, or whole text containing the variable; > > > or: > > > the most recent appearance of this variable with an explicit > > quantifier prepended; la i,n. cusku di'e > ... but there is no place in such a description where a prenex could have > occurred. If it had been {ro da poi [de zo'u:] da klama de}, fair enough, > but it appears from this that {ro klama be de} refers to all goers to one > specific place, since {de} is quantified *outside* the description, in whatever > bridi it occupies. Yes, it is. However, "ro klama" means "ro lo klama", which can be transformed WLG into "ro DA poi klama", where DA is an otherwise-unique member of the da-series. The quantification of this "DA" precedes that of "de", so the fully explicit prenex-normal-form is: ro DA [su'o] DE zo'u co'e DA poi klama de where the "co'e" represents the whole selbri in which this description is embedded. Every quantified expression in Lojban can be transformed into a form in which the quantifier is attached to a variable. Therefore, even though "de" is quantified outside the description, so is the implicit "ro DA", and the "ro DA" is outside the "de". > Is this the same as saying that there are no nested scopes? There are no nested scopes in which the same variable is rebound. There are nested scopes in the sense that within a given prenex, the variables which appear first have longer scope than those which appear later. This is not explicit or implicit in my previously-stated rules, but should have been. Likewise, when variables (actual or created by transformation) don't appear in a prenex, they are moved to the prenex in the same order in which they appear (or would appear) in the actual text. Keep asking these questions! They help concretize my ideas for a paper on the predicate logic of Lojban, one of the last unwritten papers in the reference grammar. -- John Cowan sharing account for now e'osai ko sarji la lojban.