# The Distribution Problem: An Ambiguity?

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### John Cowan

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Nov 30, 1992, 12:44:24 PM11/30/92
to Erik Rauch
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 co...@snark.thyrsus.com ...!uunet!cbmvax!snark!cowan
e'osai ko sarji la lojban.

### John Cowan

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Nov 30, 1992, 12:44:24 PM11/30/92
to Erik Rauch

### Mark E. Shoulson

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Nov 30, 1992, 5:06:40 PM11/30/92
to Erik Rauch
I don't know about historical grounds, but from my perspective of Lojban it
seems I must disagree with you, John. I agree that the current state of
affairs, leaving it ambiguous, is less than acceptable: tanruic ambiguity
does not include grouping ambiguity within the tanru.

However, it seems to me that the default grouping for logical and
non-logical connectives alike should be the non-distributive grouping.
Distributive seems convoluted and non-obvious syntactically. After all,
complex tanru, connectives or no, are interpreted as their components
modify each other as tanru elements, in the order of grouping. You don't
usually see the nature of one element affect how modifies the next larger
one. Just as {melbi cmalu nixli ckule} is {(((melbi cmalu) nixli) ckule)},
that is "((pretty type-of small [thing]) type-of girl) type-of school",
with each element modifying the next one out in "unmarked tanruic" form
(i.e. somehow having to do with), so too {cmalu je nixli ckule} must be
{(cmalu je nixli) ckule}, or "(small and girl) type-of school." The nature
of the first tanru element, that it is a logical connective, ought to have
no bearing on the fact that it simply modifies the second one in umarked
method. Thus, we have a school that is somehow associated with things that
are small-things and girlish. Similarly, (here I may be weakening my
point), {cmalu je nixli ja ckule} would be {(cmalu je nixli) ja ckule},
that is, "(small and girl) or school", so it might describe something which
is either (a) both small and girlish or (b) a school, (and possibly both).

Basically, the way tanru elements modify each other should be dependent
*only* on the various cmavo we have for just that purpose (JA, JOI, etc.)
and *not* on some magical characteristics of the elements themselves. What
would happen if we somehow crammed in a connective by means other than JA
or GUhA? Like mela'elu....li'u? Heaven only knows what's inside of that!
How do we know when (or how!) to apply distribution? If you want to throw
a cmavo in to flag distributivity, that's a different kettle of worms, and
I wouldn't mind that. I think the A je B xai C method makes the most
sense: again, we have a cmavo between tanru elements to flag the way the
modification happens.

And as for your example (1), for me, {melbi je cmalu nixli} makes eminent
sense as "(beautiful and small [thing]) type-of girl", which would likely
expand using parallel tanru method to {melbi je cmalu je nixli}, a
beautiful and small girl: a thing that is beautiful and is small and is a
girl (or, to use a sumti, {lo nixli poi ke'a melbi je cmalu}). There are,
of course other interpretations. Maybe a girl who collects
small-and-beautiful things?

~mark

### Mark E. Shoulson

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Nov 30, 1992, 5:06:40 PM11/30/92
to Erik Rauch

### b...@gnu.ai.mit.edu

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Nov 30, 1992, 9:36:22 PM11/30/92
to Erik Rauch
2) cmalu je nixli ckule
little and girl school

I read this distributively: it is a physically small school and a
school with the character of a young female. No doubt it/she is an
artificial intelligence or robot working as a school.

No joke: I was thinking `girl school, how can a school be a girl?
Ah... if it is alive; hence (since a school is not a human) it must be
an AI.'

I interpreted the tanru differently than usual, but I agree with John
Cowan ``that "A je B C" must have the distributive reading''.

Robert J. Chassell b...@gnu.ai.mit.edu
Rattlesnake Mountain Road (413) 298-4725 or (617) 253-8568 or
Stockbridge, MA 01262-0693 USA (617) 876-3296 (for messages)

### b...@gnu.ai.mit.edu

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Nov 30, 1992, 9:36:22 PM11/30/92
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### CJ FINE

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Dec 1, 1992, 1:48:18 PM12/1/92
to Erik Rauch
I agree with Bob and Nora.

John's argument assumes first that logical connectives in tanru are
distributable, and secondly that this is a syntactic rather than purely
semantic operation. I dispute both of these.

In the first place, there are several reasons for thinking that internal
connectives (jeks) cannot be factored out in the way that eks and giheks
can. (I remember somebody saying this explicitly on the net several months
ago - I think it was Bob quoting pc, but I'm not sure.)

Thus
lo nanmu je ninmu cu broda

manifestly does not have the same truth condition as

lo nanme .e le ninmu cu broda

(I got worried with this when Iain Alexander (whom I presume John means
when he says Iain Hamilton?) pointed out that

ro lo nanmu ja ninmu cu broda

means almost exactly the same as

ro lo nanmu .e ro lo ninmu cu broda
)

So even when we are not using true tanru (these are technically kanxe, not
tanru) the assumption that the connective can be distributed is false.

A fortiori, we should not expect that

melbi je nixli ckule

can necessarily be expanded to any

melbi ckule je'ipaunai nixli ckule

(Note that when the kanxe is the whole of the selbri of a bridi, expansion
does seem to be well defined; thus
ko'a broda je brode .ijo ko'a broda gi'e brode

but as I have shown, the selbri of a selgadri is just as problematic as a
seltanru or tertanru.

Secondly, the different interpretations of such connected tanru seem to me
to be well within the range of interpretations of simple tanru.

We know that
nixli ckule

could be a school for girls or, as Bob says, a school with girl-like
properties. Equally, then

cmalu je nixli ckule

which unambiguously means [cmalu je nixli] ckule,
indicates a school which is (small and girl). Whether it happens to make
sense to expand this as

cmalu ckule gi'e nixli ckule

is no more independent of the particular words used than is the question
of whether

cmalu ckule

means
ckule gi'e cmalu
or ckule belo cmalu
or even ckule befilo cmalu!

I thus argue that there is an ambiguity, but it is of the form essential
to tanru. The attempt to make such expressions formally expansible is a
chimaera, at least with our present understanding of jeks.

In passing, I disagree that "labno je remna" is a good tanru for
"werewolf". I suggest that a werewolf is neither "labno" nor "remna"
but precisely "labno joi remna".

Colin

### CJ FINE

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Dec 1, 1992, 1:48:18 PM12/1/92
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