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- Robert Goldman, compositionality
- Margaret Fleck, compositional semantics
- 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? RMail to author|Respond to list|Read more issues|LINGUIST home page|Top of issue

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 FleckMail to author|Respond to list|Read more issues|LINGUIST home page|Top of issue

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).Mail to author|Respond to list|Read more issues|LINGUIST home page|Top of issue