LINGUIST List 2.554

Wed 25 Sep 1991

Disc: Compositionality

Editor for this issue: <>

Directory

1. Erik-Jan van der Linden, compositionality
2. "Michael Kac", Re: 2.551 Compositional semantics
3. , 2.551 Compositional semantics
4. Margaret Fleck, compositionality and cardinality
5. Allan C. Wechsler, 2.551 Compositional semantics

Some additions to the compositionality debate. I focus on what
compositionality is, and hint that idioms should be drawn
into the debate (most of the stuff that follows is taken from my
PhD-thesis (in preparation)).
> Dave Chalmers talks about compositionality as a constraint and Kai von
> Fintel characterizes it as a methodological principle.
My position is that compositionality is ONE OF THE PRINCIPLES underlying
the relation between form and meaning (syntax and semantics if you like),
but that it is definitely not the only one. In the view of formal
semantics, there are compositional and non-compositional expressions, period.
However, there is more to this. Defining idioms, as is
customary throughout the linguistic literature, as expressions which
are non-compositional, is similar to defining nouns as words that are no
prepositions. Here is my definition of the PROPERTY idiomaticity
 Idiomaticity is a property of aspects of
 the meaning of complex (multi-lexemic) expressions which
 states that these aspects are exclusively a part of the meaning
 of the expression as a whole.
With this definition it is possible to classify expressions as
idiomatic or compositional, and to state WHICH aspects of an expressions
are idiomatic and which are compositional.
> one might
> try to say that one or more of the words in the idiom has a special
> meaning just in this one collocation, but that would make the semantics
> context-sensitive in some sense that people seem not to like.
Such compositional approaches (in terms of functions),
as proposed in the already mentioned
Partee (1984) and in Gazdar et al. (1985), do not work.
(for discussion, see my paper in the proceedings of the
First Tilburg Workshop on Idioms and that in COLING 1990.).
In general it is not possible to account for idioms under whatever
definition of compositionality.
> For a canonical idiom like _spill the beans_, we ought to say
> that it is analysable lexically, and that the meanings of its constituent
> parts are accessible to an etymologically-minded user.
This is not the whole story, It has frequently been pointed out that
analysability of the meaning of idioms correlates with the possibility
of idioms to occur in syntactic constructions.
The most important point to be made here is that
compositionality is ONLY ONE OF THE DESIGN PRINCIPLES of the relation
between form and meaning in natural language, besides
idiomaticity, contextuality etc. etc.
Cheers,
Erik-Jan van der Linden.

Message 2: Re: 2.551 Compositional semantics

Two quick thoughts to add to the current discussion of compositionality.
First, there has been some talk about getting a compositional semantics to
mesh with an independently motivated syntax. It's worth noting that in an
orthodox Montagovian approach, at least, there wouldn't be sucha syntax so
the issue couldn't arise. To Montague, the job of the syntax was to define
the set of meaningful expressions, so the syntax is already to at least some
degree semantics-driven.
Second, if I understand some of the remarks that have been made about ambigui-
ty, I think they are based on a confusion. Take a sentence like *The lawyer
pressed the suit* which is at least two ways ambiguous; agree for the sake of
discussion at least to localize this ambiguity in the VP, specifically in the
existence of multiple senses for *press* and *suit*. If you take Frege's
principle in a very literal, hard-headed way I think all it means is that
once you have selected senses for *press* and *suit* (do it anyway you
want), the interpretation of *press the suit* (assuming that the syntactic
structure is also specified, say via a tree or bracketing) is a function of
the meanings of these elements, the meaning of *the*, and the manner in
which they are syntactically combined. That is to say, there is a unique
meaning derivable from the meanings of the parts, once it has been decided
what meanings to assign to them. The principle of compositionality doesn't
say anything about how you assign meanings to basic expressions. A similar
observation applies in reference to deixis.
Michael Kac

Jacques Guy informs us that an infinite set of strings presupposes
either an infinite set of symbols or the existence of infinite-length
strings. This is simply false: with a finite set of symbols and no
upper bound on the length of strings, you get an infinite set of
strings. And please note: no upper bound does not mean the same
thing as infinite-length!

Jacques Guy writes:
 The set of possible expressions, utterances, what-have-you
 can be infinite
 (1) if and only if the number of language elements (phonemes,
 or morphemes or whatever, depending at what level you
 look at it) is infinite,
 OR
 (2) if and only if there exist utterances of infinite length.
This isn't quite correct. It is sufficient that there exist no finite
bound on utterance length. That is, each utterance can only be finitely
long, but utterances of any finite length are possible. This is often
expressed as: "Utterances can be arbitrarily long." It is substantially
different from saying that individual utterances can be infinitely long.
So, for example, the formal language consisting of all strings of the
form:
 I ate a dish of potstickers {and another dish of potstickers }*.
is infinite. But each sentences in it is finite, e.g.:
 I ate a dish of potstickers and another dish of potstickers.
Although you might be able to argue that there is a performance limit
on sentence length, you can find quite long examples along such patterns,
e.g. in the writing of schoolchildren attempting to pad out an essay
to a required number of words.
Margaret Fleck

In...
 Date: Mon, 23 Sep 1991 08:34 EDT
 From: The Linguist List
 <linguist%tamsun.tamu.edupucc.PRINCETON.EDU>
Jaques Guy writes:
 Alexis Manaster Ramer <USERGDD8WAYNEMTS.BITNET> wrote about
 compositionality: "...whereas the compositional rules generate
 an infinite set of expressions."
 No. The set of possible expressions, utterances, what-have-you
 can be infinite
 (1) if and only if the number of language elements (phonemes,
	 or morphemes or whatever, depending at what level you
	 look at it) is infinite,
	OR
 (2) if and only if there exist utterances of infinite length.
This inference is false. A simple counterexample: Although there are
only a finite number of digits (= language elements) and although no
decimal numeral (= utterance) is of infinite length, there are
undoutedly an infinite number of decimal numerals.
 Both conditions are contrary to fact.
Since the inference is false, the veracity of the premises doesn't
matter.
If you want to argue that the number of possible utterances is finite,
you must appeal to constraints that are violated by the "language"
consisting of all decimal numerals.
					 This point, however
 trivial, must be worth making, seeing that Langendoen and
 Postal argued in a book titled "The Vastness of Natural Language"
 that the cardinality of the set of utterances was not only
 infinite, but greater than aleph-null, aleph-one, aleph-two, in
 fact, if I remember correctly, greater than any conceivable
 transfinite number.
This is, of course, a ridiculous statement, since utterances are, at
worst, real-valued functions of air-pressure versus time; and there are
only aleph-one of those. But I have not read Langendoen and Postal.
			It is, in fact, not only infinitely smaller
 than aleph-null, but very very much smaller than one googolplex
 (but it is perhaps greater than one googol).
This is unwarranted. In fact, aleph-null is probably the correct
cardinality, assuming that "the set of possible utterances" is a valid
object of discourse.