From cbmvax!uunet!CUVMB.BITNET!LOJBAN Thu Jul 9 09:16:11 1992 Return-Path: Received: by snark.thyrsus.com (/\==/\ Smail3.1.21.1 #21.19) id ; Thu, 9 Jul 92 09:16 EDT Received: by cbmvax.cbm.commodore.com (5.57/UUCP-Project/Commodore 2/8/91) id AA16725; Thu, 9 Jul 92 08:39:31 EDT Received: from pucc.Princeton.EDU by relay1.UU.NET with SMTP (5.61/UUNET-internet-primary) id AA13929; Thu, 9 Jul 92 08:17:27 -0400 Message-Id: <9207091217.AA13929@relay1.UU.NET> Received: from PUCC.PRINCETON.EDU by pucc.Princeton.EDU (IBM VM SMTP V2R2) with BSMTP id 3065; Thu, 09 Jul 92 08:16:11 EDT Received: by PUCC (Mailer R2.08 ptf033) id 2465; Thu, 09 Jul 92 08:15:59 EDT Date: Thu, 9 Jul 1992 13:10:33 BST Reply-To: CJ FINE Sender: Lojban list From: CJ FINE Subject: Relatives and Quantifiers (Pt 1 of 2) X-To: Lojban list To: John Cowan , Eric Raymond , Eric Tiedemann Status: RO Here is the first part of the paper that apparently didn't get through a few days ago. Sumti and Relative clauses ========================== I believe there are some hidden problems with the semantics and syntax of relative clauses and quantifiers. In this paper I discuss the problems, and suggest some solutions. 1. Relative clauses ------------------- The syntax of relative-clauses is: relative_clause_110 : relative_clause_A_111 | relative_clause_110 ZIhEK_820 relative_clause_A_111 i.e., a constituent consisting of a left- associative list of individual relative clauses. I believe this is a faulty analysis. To see where the problem lies, consider a relative clause as a semantic operator: it takes as its argument (the referent of) a sumti - some more or less specified set of entities - and delivers another set (or a sumti which refers to this set - it doesn't matter very much whether we take the operator as acting on sumti or their referents). In the case of an incidental relative (ne, noi, goi), the membership of the result set is identical to that of the argument set - all we have done is made a subsidiary claim about its members. eg lo sipna = [some of] all sleepers lo sipna noi melbi = [some of] all sleepers, by the way, they (all sleepers) are beautiful ('some of' is not relevant to the argument here, but is implicit in the meaning of "lo" - in fact it represents a subsequent operation on the sumti which I will come to below). The set of all sleepers is selected by "lo sipna", and unchanged by the incidental relative. A restrictive relative, on the other hand, in general delivers a different set from its argument. e.g. lo sipna = [some of] all sleepers lo sipna poi melbi = [some of] all those sleepers who are beautiful. Clearly each successive restrictive will deliver a further altered set: lo sipna poi melbi zi'e poi mi prami ke'a = [some of] {{all those sleepers who are beautiful} whom I love} and logically we have a left-associative structure in which the relative-clauses is not an independent constituent. Thus far, I have established that the grouping in the Lojban syntax is logically erroneous; but this might not be very important. The next sections show how it does matter. 2. Mixed relatives ------------------ First, note that incidental relatives certainly associate (in fact, commute): lo sipna noi melbi zi'e noi vasxu "sleepers, who are beautiful, and who breathe" does not depend on any grouping, and is even the same (except maybe for some pragmatics) as lo sipna noi vasxu zi'e noi melbi Probably, the same is true for restrictives: lo sipna poi melbi zi'e poi mi prami ke'a probably always delivers the same set as lo sipna poi mi prami ke'a zi'e poi melbi. (I am not convinced this is always true). The first problems appear when we mix the two. Does lo sipna poi mi prami ke'a zi'e noi melbi mean the same as lo sipna noi melbi zi'e poi me prami ke'a? As far as I know, the answer is not currently defined in Lojban. I believe that the first is (or should be) saying (incidentally) that all the sleepers that I love are beautiful, whereas the second says that all sleepers are beautiful, even though it is then going on to talk about only those whom I love. Though this *is* a problem, I don't think it is a big one, mainly because the only common occasion for mixing the two has been with "goi": le prenu goi ko'a zi'epoi mi viska ke'a vs le prenu poi mi viska ke'a zi'egoi ko'a "The people whom I saw, (henceforward x1)" and even there, the technical difference (whether x1 refers to all people or just the one(s) I see) is often vitiated by the intensionality of "le" as opposed to "lo". If this were all, we could probably get by with the existing syntax, and adding one of two interpretative rules to the (pu'o) semantics: Either: "Take the relative clauses in order; each restrictive clause selects some subset from the current set of designated entities and makes that the current set; each incidental clause makes that subsidiary remark about the current set" or, more simply: "Take all the restrictive clauses together and apply them to get the final set; then interpret each incidental clause as commenting on that final set" which is certainly simpler, though very grubby. 3. External quantifiers ----------------------- Where the problem starts to become bigger is with quantifiers. There are actually two semantically different occurrences of these, which I shall call "external" and "internal". Internal quantifiers are within descriptions, considered below in section 4. External quantifiers occur in rule sumti_D_95 : sumti_E_96 | quantifier_300 sumti_E_96 (and also in indefinite sumti, which I will come to below), and I suggest that they are semantically similar to a restrictive clause. That is to say, ci lo cukta "three books" is roughly equivalent to something like lo cukta poi lu'i roke'a cu cimei "books such that the set of all of them is a threesome" (I am not claiming that this is a precise paraphrase, or a transformation; my point is that, like a restrictive clause, the quantifier performs a substantive selection operation on the set of referents). In fact, external quantifiers do not bind as tightly as restrictive clauses, so a phrase like ci lo sipna poi melbi means three of (those sleepers who are beautiful), and the current parse ci [[lo sipna] [poi melbi]] corresponds with this interpretation. But if we then introduce incidental relatives, the current syntax does not give the right answer. Thus: ci lo sipna noi melbi currently parses as ci [lo sipna noi melbi] three out of [all sleepers, who incidentally are all beautiful] but I believe that almost all seljbo would interpret it as [ci [lo sipna]] [noi melbi] [three out of all sleepers], who are beautiful. Similarly with quantifiers and both types of relative: ci lo sipna goi ko'a zi'epoi mi nelci ke'a The current syntax makes this ci [lo sipna [goi ko'a zi'epoi mi nelci ke'a]] i.e. ko'a is either all sleepers, or all the sleepers I like, but in no way just three of them. [The "some of" in the early examples belongs here, as it is the default external quantifier for "le" and "lo".] In summary, incidental relatives belong outside the external quantifier, but restrictive ones belong inside. 4. Internal quantifiers ----------------------- When we look inside a description we get a different kind of quantifier, with different properties: le ci sipna the three sleepers It seems to me that this is semantically an incidental rather than a restrictive construction. As I understand it lo vo prenu makes the subsidiary claim that there are only four persons, which is an incidental claim to the description, and not a restriction. This does not give any problem with explicit incidental clauses: lo mo'a temci noi sutra simci the too-few time intervals (that seem fast) but the interaction with explicit restrictives is wrong: le ci sipna poi mi nelci ke'a is at present unequivocally [le ci sipna] [poi mi nelci ke'a] those among [the three sleepers] whom I like whereas what it should mean is le ci [sipna poi mi nelci ke'a] i.e. the sleepers that I like, of whom there are in fact three. So as with external quantifiers, incidental relatives belong outside, but restrictive ones belong inside. [Continued in subsequent mailing]