LINGUIST List 2.523

Tue 17 Sep 1991

Disc: Compositional Semantics

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1. David Chalmers, Re: 2.507 Compositional Semantics
2. , Re: 2.514 Compositional Semantics
3. , Compositional Semantics
4. Margaret Fleck, compositional semantics

Message 1: Re: 2.507 Compositional Semantics

The compositionality "constraint" that the meaning of the sentence be a
function of the meaning of its parts is hardly a constraint at all. All
this implies is that given two sentences whose parts have identical meanings,
then the sentences have identical meanings. This very weak property is
satisfied by all kinds of languages that we don't want to call compositional
(e.g. a language in which "trees", "are", and "green" mean what they do
in English, but in which "trees are green" means "the quarterback fainted
last Saturday").
Presumably, to capture the intuitive notion of compositionality, we have
to strongly constrain the class of functions involved, so that sensitivity
to particular part-meanings on a case-by-case basis is barred, and the
function is forced to be "general" in some sense to be specified. On
the other hand, we don't want to disallow all casewise sensitivity --
our function presumably has to be sensitive to certain information about
category membership of the individual parts. Maybe what compositionality
comes down to is that the number of cases must be small relative to the
number of possible constituents, and that the function must possess a brief
specification.
Dave Chalmers.

Message 2: Re: 2.514 Compositional Semantics

I don't see how idioms can be used as an argument against compositionality.
What makes something an idiom is the fact that there is a discrepancy between
its literal (compositional) meaning and the conventional meaning. You have to
have the compositional meaning to know that something is an idiom. Moreover,
the compositional meaning must be unambiguous. "To break the bank" does not
evoke pictures of river banks, and "to cry wolf" does not contain the same
sense of 'cry' as "to cry over spilled milk". Even though the metaphor
underlying the idiom may be brain-dead, the body still lives on.
Alexis makes some interesting points about compositional semantics and its
incompatibility with information loss. He used the example of 'dogs' being
derived by subtraction of the singular marking on the stem. The example
doesn't work so well for me, since one could claim that singular stems don't
exist, but singularity is *added* with a null suffix. However, there are
examples of affixes that truly do subtract meaning--e.g. decausativizing
suffixes that create intransitive verbs from transitive stems. But I see no
problem at all for the notion of compositionality. Adding structure
need not always be equated with adding positive semantic value to the
base. After all, we get subtraction when we add negative numbers to positives.
				-Rick Wojcik (rwojcikatc.boeing.com)

With respect to the discussion about compositionality and specifically in
reply to Alexis Manaster-Ramer's posting in 2.514:
For most formal semanticists compositionality is a methodological guideline:
make your semantics compatible with an independently motivated syntactic
analysis; if that is impossible, motivate an alternative syntactic analysis
with syntactic arguments. As such the principle is of course more
interesting and challenging than any a priori conviction that it must be
wrong. It will be interesting to see where real emprircal problems arise. For
a nice discussion of some hard problems see Barbara Partee's 1984 paper
"Compositionality".
Of the specific problems raised in this discussion, idioms should probably be
left aside (I agree on this with Richard Coates). For the problem with plurals
(the subject of a thriving debate in formal semantics), there are two
immediate options to consider:
(i) The less interesting one claims that there is in fact a zero morpheme
 converting "dog" into "dog sg.". Then nothing gets erased by the plural
 morpheme. While this may be the correct way to go, there is a more
 basic answer:
(ii) It is entirely conceivable that the semantics given to a plural common
 noun like "dogs" is in fact the result of a pluralisation operation
 applied to the meaning of "dog sg.". Simplistically, if "dog" denotes
 the set containing all dogs, say {Fido, Spot, Rex}, then "dogs" could
 denote the power set of that set minus the empty set and minus the
 singletons, i.e. {{Fido, Spot}, {Fido, Rex}, {Spot, Rex}, {Fido, Spot,
 Rex}}. This is of course an easily defined operation. Nothing gets
 lost or erased. Much more sophisticated discussion is found in the
 work of Godehard Link, Fred Landman, Roger Schwarzschild, etc.
Kai von Fintel, Dept. of Linguistics, UMass Amherst.
FintelLinguist.Umass.edu

The use of the term "function" in some previous messages on
compositional semantics, though perhaps traditional, is a bit
dangerous, as it seems not to agree with the use of the term in
mathematics. Consider, for example,
 Within this camp "compositionality" has a precise meaning---a semantic
 interpretation function is compositional iff the interpretation of a
 syntactically complex constituent depends functionally on the
 interpretation of its constituents.
 --- "John Nerbonne" <nerbonnedfki.uni-sb.de>
 I think it deserves to be pointed out that technically compositionality
 has the effect of requiring that every syntactic structure be semantically
 unambiguous. Otherwise, the word 'function' in the usual definition of
 compositionality would have to be replaced by the word 'relation'.
 --- Alexis_Manaster_Ramermts.cc.wayne.edu
Well, actually, you can build a function deriving the meaning of a
constituent from the meanings of its subparts, even if there is
ambiguity. Let f be a function deriving the meaning, assuming there
is no ambiguity. Then, represent an ambiguous constituent A as a set
of meanings mA = {ma1, ma2, ...., man}. The meaning of the unit A
combined with some (unambiguous) unit B (with meaning mB = {mb}) would
then be F(mA, mB) = {f(ma1,mb), f(ma2,mb), ...., f(man,mb)}. This
extends in an obvious way to the case where both contituents are
ambiguous. Mathematically, F is just as good a function as f.
Worse, there is nothing mathematically preventing a function from
using one strategy to compute the meaning of e.g. NP plus VP in
general, but a TOTALLY DIFFERENT method of computing it when given
some particular lexical items, e.g. kick plus bucket.
I really doubt that either "being a function" or "being a computable
function" is really the important issue here. I would have thought
that all vaguely presentable semantic theories could be gotten to look
mathematically like (computable) functions. Therefore, it seems like
a definition for "compositionality" would have to discuss, rather, the
constraints on what *types* of functions are allowed, e.g.
 -- the degree of ambiguity permitted,
 -- the form of the meaning representations being passed upwards (e.g.
 limits on free variables in them), and/or
 -- some constraint that functions must (at least usually) operate on
 their arguments in a REGULAR way.
Margaret Fleck