LINGUIST List 2.551

Mon 23 Sep 1991

Disc: Compositional semantics

Editor for this issue: <>

Directory

1. Robert Goldman, compositionality
2. Margaret Fleck, compositional semantics
3. Jacques Guy, Compositionality: the smallness of natural language

I am somewhat confused by your argument
>	Let us suppose that expression E consists
>	of constituents C1...Cn arranged in structure X.
>	If E is ambiguous between meanings M1 and M2, then
>	we cannot say that f(C1...Cn, X) = M1 AND that
>	f(C1...Cn, X) = M2, for then f would not be a
>	function and the semantics would not be compositional.
>	Therefore let us say that f(C1...Cn, X) = {M1, M2}.
>But this presents a weird view of ambiguity. It says that an
>ambiguous expression has ONE meaning, M1-and-M2. In contrast,
>what we want is a theory that says an ambiguous expression
>means M1 OR M2.
Why does it follow necessarily that {M1,M2} must be interpreted as an
implicit CONjunction rather than an implicit DISjunction? What makes
it difficult to have "a theory that says an ambiguous expression means
M1 or M2?
R

Two brief replies:
To Paul Saka: There is no reason why a semantic representation of the
 form {M1, M2} has to mean M1-and-M2, except perhaps within the context
 of some very specific theory of semantics. It can equally well mean
 M1-or-M2. The mathematical object, by itself, does not specify any
 particular interpretation. Using sets to represent OR's of several
 possibilities is a reasonably traditional tactic in AI reasoning systems.
 It lends itself to obvious implementations in which the sets are stored
 as lists and, when a possibility is ruled out by additional information,
 it is removed from the appropriate list(s).
To Alexis Manaster Ramer: I agree with you that sets of meanings are
 not something we *want* to allow, but I think they may be fairly
 difficult to forbid formally. Notice that my construction does not
 really require sets: I could do exactly the same thing with functions
 that produce a single form, but a form that consists of a string of
 meanings joined by OR. I think one could wriggle out of the obvious
 next patch, a constraint that the top of the form not be an OR, by pushing
 the offending OR further into the form. One could prohibit OR's
 totally (i.e. even within subparts of the form), but I'm not sure
 that isn't too strong. (Or is it?)
 On the other hand, your idea of requiring non-destructiveness does seem
 potentially useful, and potentially formalisable (at least within a given
 specific theory). Compare Marcus's theory of NL parsing.
Margaret Fleck

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.
Both conditions are contrary to fact. 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. 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).