The Distribution Problem: An Ambiguity?

[John Cowan <cbmvax!snark.thyrsus.com!cowan@UUNET.UU.NET>]

In the course of writing a paper on the structure of Lojban selbri
(Jimbobs and old-timers will recognize the phrase "pretty little
girls' school" as relevant), I have come across what I believe to be
a fundamental ambiguity in the interpretation of certain complex tanru.
This ambiguity was first pointed out to me by Iain Hamilton; I researched
it in JCB's various publications on the subject and those of other Loglanists,
and finally checked with lojbab and Nora.  I conclude that the ambiguity is
real and needs a resolution of some sort.  Comments are urgently solicited.

The simplest type of tanru that exposes the problem is "A je B C", an
A-and-B type of C.  Examples:

1)      melbi je cmalu nixli
        pretty and little girl

2)      cmalu je nixli ckule
        little and girl school

3)      labno je remna dapma
        wolf and man curse
        werewolf curse

Each of these tanru is susceptible of two different interpretations, which
I call "distributive" and "non-distributive".  In the distributive
interpretation, "A je B C" means "(A B) je (A C)"; in the non-distributive
interpretation, it means "C of type A-je-B".

Example (1) probably prefers the distributive interpretation: a pretty and
little girl is something which is both a pretty girl and a little girl.
I call this "distributive" by analogy with the distributive law in
mathematics, which tells us that (A + B) * C = (A * C) + (B * C).
Indeed, it is hard to see a reasonable English sense for the non-distributive
interpretation.

Example (3), on the other hand, prefers the non-distributive interpretation.
In this case, "A je B" is taken as a basic tanru which as a whole modifies C.
"labno je remna" is a reasonable tanru for "werewolf"; it describes something
which is both a human being and a wolf.  (Etymologically, the "were-" part of
the English word also means "remna", or perhaps "nanmu".) So a "werewolf curse"
is not something which is both a wolf curse and a human curse, but rather a
curse associated with something which is both a human being and a wolf.

Example (2) can readily be read both ways.  Is the school in question one
which is both a little school and a girls' school, or is it one which is
for creatures who are both little and girls?

My historical investigation (Loglan 1, 3rd and 4th editions, plus the
intervening issues of The Loglanist) establishes that JCB always takes the
distributive interpretations.  He understands "A je B C" as a mere
abbreviation for "A C gi'e B C".  For him (and a fortiori, for pc at the
time in question), "A je B" as a stand-alone tanru is so-called "bad usage"
(that is, permitted by the machine grammar but forbidden by a side
constraint); he consistently uses "A gi'e B" in all such circumstances.
Lojban does not have the concept "bad usage": what the machine grammar
allows is grammatical tout court.

pc does make the comment (TL4/1:49) that "X is a quick-if-red fox" is
not the same as "X is a quick fox if X is a red fox" because the former
asserts that X is a fox, whereas the latter is a mere implication that
makes no such assertion.  As long as we confine ourselves to "je" and "ja",
however, this distinction is immaterial.

When I spoke by telephone with Bob and Nora, their view (as best I understood
it) was that the ambiguity was real but acceptable, given that only tanru
are involved, tanru being inherently ambiguous.  I disagree.  My view is that
ambiguities that involve >grouping< are not allowed in the language --
the purpose for "ke...ke'e" and "bo" mechanisms" -- and that the
distributive vs. non-distributive distinction is, in fact, one of grouping.

Iain Hamilton proposed a clever resolution based on Backus FP, which I
regretfully reject as too unLojbanic.  Nora suggested the use of "joi"
to force the non-distributive reading (and "ku'a", set intersection,
might serve the same purpose); unfortunately, there are 14 logical
connectives, and not enough non-logical ones to go around.

A formal device that would certainly work, but would be both a grammar
change and a major change in thinking, is to introduce one or two new cmavo.
Either a cmavo for "distributive", or one for "non-distributive", or one
for each meaning may be introduced; in the last case, the unmarked situation
remains ambiguous.

A few possible syntaxes:

        A xai je B C            [infix after connective]
        A je xai B C            [infix before connective]
        A je B xai C            [suffix, or can be seen as infix
                                        between "A je B" and "C"]
        xai A je B C            [prefix]
        xai A je B [xa'i] C     [paired delimiters]

I don't like any of this.  If new syntax is truly required, I believe the
demands of history are such that "A je B C" must have the distributive
reading unless a compelling case can be made otherwise.  As second best,
let it remain ambiguous but provide some way (by syntax or otherwise) of
disambiguating.  Taking "A je B C" as non-distributive only seems to me
perverse.

--
John Cowan      cowan@snark.thyrsus.com         ...!uunet!cbmvax!snark!cowan
                        e'osai ko sarji la lojban.