From LOJBAN%CUVMB.bitnet@YaleVM.YCC.YALE.EDU Sat Mar 6 22:54:49 2010 Received: from YALEVM.YCC.YALE.EDU by MINERVA.CIS.YALE.EDU via SMTP; Tue, 16 Mar 1993 00:34:13 -0500 Received: from CUVMB.CC.COLUMBIA.EDU by YaleVM.YCC.Yale.Edu (IBM VM SMTP V2R2) with BSMTP id 0492; Tue, 16 Mar 93 00:33:02 EST Received: from CUVMB.BITNET by CUVMB.CC.COLUMBIA.EDU (Mailer R2.07) with BSMTP id 7032; Mon, 15 Mar 93 19:13:12 EST Date: Mon, 15 Mar 1993 16:12:49 -0800 Reply-To: jimc@MATH.UCLA.EDU Sender: Lojban list From: jimc@MATH.UCLA.EDU Subject: Re: TECH: Linguistics and x1/Subject ellipsis X-To: lojban@cuvmb.columbia.edu To: Erik Rauch In-Reply-To: Your message of "Mon, 15 Mar 93 12:29:15 EST." <9303151938.AA01227@julia.math.ucla.edu> Status: OR X-From-Space-Date: Mon Mar 15 08:12:49 1993 X-From-Space-Address: @YaleVM.YCC.YALE.EDU:LOJBAN@CUVMB.BITNET Message-ID: Lojbab writes: > I realize that jimc has proposed an analysis of omitted places involving > "auto-replication", which I have never really understood.... John Cowan has been saying something very similar in terms of lambda calculus and propositional functions. I suppose this is the language by which logicians think of such matters, and it certainly has a solid ring to it: LAMBDA CALCULUS :-) Anyway: Consider a restrictive subordinate clause: lo mlatu poi (ke'a) xekri a cat r.c. {(it) is black} What's black, and how do you know? In the vacant x1 (after conversion) of the clause, a pronoun ke'a is assumed present according to rules, and this pronoun is bound to "lo mlatu". The effect is that proposed referents of "lo mlatu" are replicated into the clause, and because it's restrictive, only the ones for which the clause is true are retained. That's what replication means. In terms of propositional functions, {(it) is black} is a function which does not contain its own sumti; its argument is bound to another sumti, "lo mlatu". Points important to me: a. The occupant of this vacant place is an invisible pronoun. b. Presence of this pronoun is required by rules (except for exceptions...) c. The binding target of the pronoun is specified by rules. Now I apply the same concept to abstractions, stealing the same pronoun. I may not be totally up to date on the latest place structure proposal; I am assuming that binxo x2 expects a property abstraction for what x1 becomes. le mlatu binxo lo ka (ke'a) blabi the cat becomes { (it) is white } Again, identically with the subordinate clause, I want the vacant x1 place of the abstraction to be occupied by an invisible ke'a which is bound to "le mlatu". But since this is an abstraction, not a subordinate clause, the binding target is binxo x1. Now I want all this to happen because of rules -- I don't want users to have to glork this by mental telepathy. Clauses have only one possible binding arrangement whereas abstractions are more complicated. Nonetheless I allege that relatively simple rules will be sufficient. Most cases are covered by this rule: bind the abstraction's ke'a to the previous place (before conversion) of the containing bridi. This rule would work even better if place definitions were adjusted correspondingly. Such a rule for "replicating" (or binding) neighboring sumti into an abstraction would greatly ease our semantic problems in interpreting abstractions; would allow clear and non-vague interpretations of many tanru; and would allow definite meanings to be ascribed to lujvo based on those tanru. -- jimc