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Re: anaphor means what? (was: oops! correction)
>> From: jimc@edu.ucla.math
>> Date: Fri, 26 Apr 91 09:46:21 +0100
> Date: Thu, 25 Apr 91 10:23:38 +0100
> To: lojban-list@snark.thyrsus.com
> From: David Elworthy <David.Elworthy@computer-lab.cambridge.ac.uk>
> Subject: Re: anaphor means what? (was: oops! correction)
>> ...interpreting anaphors by copying the words of the antecedent. This
>> is an approach which was suggested by linguists some time ago, and which
>> has been firmly rejected. What is wrong with it?
> You need a commitment (which English doesn't give) that the copied words
> have the same referent in their new home. In other words:
> Every farmer who owns (a donkey) beats (a donkey) [must transform to]
> All F, ((F is a farmer) and (exists D) and (D is a donkey) and
> (F owns D)) implies (F beats D) [the same D]
Interestingly, this is exactly the approach taken by Groenendijk and Stokhof,
in their Dynamic Predicate Logic (DPL). Here, a variable introduced by an
existential quantifier remains bound even outside the normal scope of the
quantifier. The binding is terminated by negation and universal
quantification, to prevent things like:
Every farmer who owns a donkey beats it. ?It neighs.
which is found to be unacceptable by most people, except when you imagine that
the second sentence is somehow still within the scope of the "every". (The
unacceptability isn't too clear here, I know: please take it for granted that
the general evidence is that you can't have a singular anaphor in later
sentences.)
A problem possibly arises with this:
Every farmer who owns a donkey beats it. They neigh.
What seems to be happening here is that we have "summed" over all the "D"s. It
may be clearer in the example with "Most farmers" in place of "Every farmer".
[1]. You can solve this in the DPL approach, but it's a bit messy: the
"summation" process gets defined as an operator on the interpretation of the
formula, rather than an operator in the formula. An alternative is to replace
D by a function, giving you:
All F, Exists D, ((F is a farmer) and (D(F) is defined)
and (D(F) is a donkey) and (F owns D(F))) implies
(F beats D(F))
The disadvantage here is that you need to go to a higher-oreder logic,
involving quantification over sets (or functions) with all the problems that
introduces.
-----
>> The copying problem can also be seen in another classic sentence,
>> known as the Bach-Peters paradox:
>>
>> (6) The boy who deserves it will get the prize he wants.
> The infinite regression is a definite problem which I have already had to
> solve by ugly hacks in [my] transformation program. And even if referents
> are copied, not words, it looks to me as if you still have an infinite
> loop.
Try widening the quantifiers:
(The b) (The p) [boy(b) & deserve(b,p) & will-get(b,p) and want(b,p)]
where "The b" means "there is a definite b such that..."
-----
>> The conclusion from this is that the interpretation of anaphors is *not*
>> the business of the parser, or of the syntactic component in any sense.
[...]
> But that's because English is a pile of junk,
> not an intrinsic feature of anaphora.
Well, actually, I find English beautiful and difficult, which I why I do my
research on it.
> I would ascribe anaphor resolution to a "transformation" phase that
> follows syntax analysis and precedes semantics. My motivation is to
> feed into the semantic analyser a uniform set of "deep structures".
> Obviously :-), anaphora are irrelevant and have to be transformed away
> first. That is, "every farmer with a donkey beats IT" is semantically
> identical to "every farmer with a donkey beats THE DONKEY" as well as to
> the selected-by-me deep structure (all F|farmer exists D (D is donkey and
> F owns D implies F beats D)).
OK, but I would call your "transformation" phase part of the semantics. Note
that the semantic analyser does have to feed information back up to it, so it
can resolve inter-sentential anaphors (assuming you feed in one sentence at a
time, rather than process the whole discourse).
I don't think that all problems of anaphora can be solved purely in semantics.
They certainly can't be at present, although formal theories of anaphora are
getting better all the time. But there will always be cases where some fairly
vague inference schemas are needed, as in
John is a guitarist because he thinks it is a beautiful instrument.
You might also like to know that in at least one large-scale NL processing
system, namely SRI's Core Language Engine, the anaphor resolution is done
after the rest of the semantics: a so-called "quasi logical form" is
constructed, with place markers for the anaphors.
-----
I think my earlier reply was probably rather negative. I'm not aiming to
attack Lojban or any of the people who are working on it - it's just that I
have spent some time studying this field, and I see some danger that Lojban
will take an approach which is known to have problems with it.
[1] This is off the point, so I've put it in a footnote. Dou you know how
Lojban handles the semantics of "most"? If it is done by a quantifier similar
to "exists" or "all", be warned that it can be shown this will not work! I'll
forward details if you're interested.
-- jimc