Relatives and Quantifiers (Pt 1 of 2)

[CJ FINE <cbmvax!uunet!BRADFORD.AC.UK!C.J.Fine>]

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]