Received: from ELI.CS.YALE.EDU by NEBULA.SYSTEMSZ.CS.YALE.EDU via SMTP; Tue, 15 Feb 1994 10:52:24 -0500 Received: from YALEVM.YCC.YALE.EDU by eli.CS.YALE.EDU via SMTP; Tue, 15 Feb 1994 10:52:19 -0500 Message-Id: <199402151552.AA04464@eli.CS.YALE.EDU> Received: from CUVMB.CC.COLUMBIA.EDU by YaleVM.YCC.Yale.Edu (IBM VM SMTP V2R2) with BSMTP id 0057; Tue, 15 Feb 94 10:50:28 EST Received: from CUVMB.COLUMBIA.EDU by CUVMB.CC.COLUMBIA.EDU (Mailer R2.07) with BSMTP id 4960; Tue, 15 Feb 94 10:50:37 EDT 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: Erik Rauch In-Reply-To: <9402151311.AA26953@getafix.oasis.icl.co.uk> from "i.alexander.bra0125@oasis.icl.co.uk" at Feb 15, 94 01:11:43 pm Status: RO X-Status: X-From-Space-Date: Tue Feb 15 05:49:59 1994 X-From-Space-Address: @YaleVM.YCC.YALE.EDU:LOJBAN@CUVMB.BITNET 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.