Alternating Quantifier Scope in CCG

Alternating Quantifier Scope in CCG* Mark Steedman Division of Informatics, University of Edinburgh, 2 Buccleuch Place, Edinburgh EH8 9LW, UK steedman@cogsc i. ed. ac. uk Abstract The paper shows that movement or equivalent computational structure-changing operations of any kind at the level of logical form can be dispensed with entirely in capturing quantifer scope ambi- guity. It offers a new semantics whereby the ef- fects of quantifier scope alternation can be obtained by an entirely monotonic derivation, without type- changing rules. The paper follows Fodor (1982), Fodor and Sag (1982), and Park (1995, 1996) in viewing many apparent scope ambiguities as arising from referential categories rather than true general- ized quantitiers. 1 Introduction It is standard to assume that the ambiguity of sen- tences like (1) is to be accounted for by assigning two logical forms which differ in the scopes as- signed to these quantifiers, as in (2a,b): 1 (1) Every boy admires some saxophonist. (2) a. Vx.boy' x -+ 3y.saxophonis/ y A admires' yx b. 3y.saxophonis/ y A Vx.bo/x -+ admires'yx The question then arises of how a grammar/parser can assign all and only the correct interpretations to sentences with multiple quantifiers. This process has on occasion been explained in terms of "quantifier movement" or essentially * Early versions of this paper were presented to audiences at Brown U., NYU, and Karlov2~ U. Prague. Thanks to Jason Baldridge, Gann Bierner, Tim Fernando, Kit Fine, Polly Ja- cobson, Mark Johnson, Aravind Joshi, Richard Kayne, Shalom Lappin, Alex Lascarides, Suresh Manandhar, Jaruslav Peregrin, Jong Park, Anna Szabolcsi, Bonnie Webber, Alistair Willis, and the referees for helpful comments. The work was supported in part by ESRC grant M423284002. tThe notation uses juxtaposition fa to indicate application of a functor f to an argument a. Constants are distinguished from variables by a prime, and semantic functors like admires' are assumed to be "Curried". A convention of "left associativi- ty" is assumed, so that admires'yx is equivalent to (admires'y)x. equivalent computational operations of "quantify- ing in" or "storage" at the level of logical form. However, such accounts present a problem for monostratal and monotonic theories of grammar like CCG that try to do away with movement or the equivalent in syntax. Having eliminated non- monotonic operations from the syntax, to have to restore them at the level of logical form would be dismaying, given the strong assumptions of trans- parency between syntax and semantics from which the monotonic theories begin. Given the assump- tions of syntactic/semantic transparency and mono- tonicity that are usual in the Frege-Montague tra- dition, it is tempting to try to use nothing but the derivational combinatorics of surface grammar to deliver all the readings for ambiguous sentences like (1). Two ways to restore monotonicity have been proposed, namely: enriching the notion of deriva- tion via type-changing operations; or enriching the lexicon and the semantic ontology. It is standard in the Frege-Montague tradition to begin by translating expressions like "every boy" and "some saxophonist" into "generalized quanti- tiers" in effect …

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