LINGUIST List 2.619

Mon 07 Oct 1991

Disc: The Finiteness of Language; Features

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1. , 2.602 Is Language Finite?
2. Mark Johnson, Re: 2.568 Features
3. , Re: 2.568 Features

(1) I don't see how Tom Lai gets the result that languages whose
sentences are made up of words taken from an infinite lexicon are
necessarily uncountably infinite. I can have a (countably) infinite
lexicon and a syntax of the form S -> w, where w is any word in
the lexicon. The language will then be the same as the lexicon,
viz., countable. I can also concatenate all the words in the
lexicon into a single string of countably infinite length (Langendoen
and Postal of course allow even greater lengths!), then the language
will be finite!
(2) I was really happy to see Terry Langendoen present the case
for transfiniteness the way he does (as a theoretical simplicity
argument). It does seem as though in the published works the
argument was presented as a proof about the properties of a real-
world object, namely, English. This distressed many readers,
I think, since cannot state theorems about English and since the
size of the real-world object in question did not seem to be
a question subject to testing.
It is also of capital importance that Terry now separates the
issue of Platonism vs. conceptualism from the question of size of
NLs. But I for one would be interested to know whether he therefore
no longer disagrees with conceptualism or whether he finds other
arguments against conceptualism more compelling.
(3) And I cannot resist adding that this very important statement
from Langendoen is a perfect example of the kind of useful function
that LINGUIST has been performing.

Message 2: Re: 2.568 Features

 From: Linguist List: Vol-2-568.
 WHEATLJSibm3090.computer-centre.birmingham.ac.uk asks
> Yes but ... is this in aywa connected with
> what ordinary people do with language
> ... John Wheatley
Underneath all the algebra and logic of the disjunctive
feature structure work I think there is an intuition that
many ambiguities are essentially _local_ in nature, and that
rather than always "multiplying out" these ambiguities,
it should possible to keep at least some ambiguities local,
and avoid an exponential explosion in the number of
analyses. Right now our understanding of how to do
this is still fairly primitive (despite all the fancy
jargon!), but I think ultimately we would like to
obtain a parse representation that says something like (say)
"In this sentence, PP_1 is either modifying VP_2 or NP_3,
and the quantified NP_4 may optionally take scope over NP_5;
if it does then the pronoun NP_6 is contra-indexed with NP_4".
Right now, most parsers would produce a set of the parse trees
that enumerate all of these possibilities.
Aside from its exponential size, such a set of parse trees is
also really not so good as an input for semantic/pragmatic
processing if we take it that one of the things these components
do is disambiguate syntactic ambiguities. This is because
such a disambiguator really isn't concerned with the "semantic
value" of each individual parse tree; what it really needs to
know is how the various possible syntactic analyses minimally
differ from each other, which is what these disjunctive representations
provide.
This is a fairly tricky area, and I would like to see more
psycholinguistic work done to see how the one type of
fully-functional Natural Language Understanding systems (the one in
the human mind) solves this problem. Kurt Vanlehn's MIT thesis
suggests that humans can delay deciding quantifier scopes
in many situations, and I've heard proposals that PP attachment
may also in general not be resolved. Note that if they are to
be taken seriously, these proposals cannot mean that the PP is
literally unattached (otherwise how does it contribute semantically
to the utterance, or why isn't it interpreted as potentially
modifying all NPs and VPs in the sentence).
Mark Johnson

Message 3: Re: 2.568 Features

>Yes but what has this to do with the cost of bread
>or to paraphrase - is this in aywa connected with
>what ordinary people do with language
>can all this Boolean logic contribute somewhere or is
>it just cleverness for its own sake - linguistics
>away from the social or even the psychological?
>I do not mean to be disrespectful - I just wonder!
>John Wheatley
Before we start studying what ordinary people do with language in any
detail, it seems useful to characterize the regularities of language
itself. For that purpose feature structures are a very useful tool. As a
linguist I certainly want to know as much as possible about the
mathematical properties of and inherent possibilities in the formal tools I
am using.
Helge Dyvik