Quantifier Scope and Constituency

Quantifier Scope and Constituency Jong C. Park Computer and Information Science University of Pennsylvania 200 South 33rd Street, Philadelphia, PA 19104-6389, USA park@line, cis. upenn, edu Abstract Traditional approaches to quantifier scope typically need stipulation to exclude rea- dings that are unavailable to human under- standers. This paper shows that quantifier scope phenomena can be precisely charac- terized by a semantic representation cons- trained by surhce constituency, if the di- stinction between referential and quantifi- cational NPs is properly observed. A CCG implementation is described and compared to other approaches. 1 Introduction It is generally assumed that sentences with multi- ple quantified NPs are to be interpreted by one or more unambiguous logical forms in which the scope of traditional logical quantifiers determines the rea- ding or readings. There are two problems with this assumption: (a) without further stipulation there is a tendency to allow too many readings and (b) there is considerable confusion as to how many readings should be allowed arising from contamination of the semantics of many NL quantifiers by referentiality. There are two well-known techniques for redis- tributing quantifiers in quantification structures: quantifying-in (Montague, 1974; Cooper, 1983; Kel- ler, 1988; Carpenter, 1994) and quantifier raising (May, 1985). The former provides a compositio- nal way of putting possibly embedded quantifiers to the scope-taking positions, and the latter utili- zes a syntactic movement operation at the level of semantics for quantifier placement. There are also approaches that put more emphasis on utilizing con- textual information in restricting the generation of semantic forms by choosing a scope-neutral repre- sentation augmented with ordering constraints to capture linguistic judgments (Webber, 1979; Kamp, 1981; Helm, 1983; Poesio, 1991; Reyle, 1993). And there are computational approaches that screen una- vailable and/or redundant semantic forms (Hobbs Shieber, 1987; Moran, 1988; Vestre, 1991). This pa- per will show that these approaches allow unavaila- ble readings, and thereby miss an important gene- ralization concerning the readings that actually are available. This paper examines English constructions that allow multiple occurrences of quantified NPs: NP modifications, transitive or ditransitive verbs, that complements, and coordinate structures. Based on a critical analysis of readings that are available from these data, the claim is that scope phenomena can be characterized by a combination of syntactic sur- face adjacency and semantic function-argument re- lationship. This characterization will draw upon the old distinction between referential and quantificatio- nal NP-semantics (Fodor & Sag, 1982). We choose to use Combinatory Categorial Grammar to show how surface adjacency affects semantic function- argument relationship, since CCG has the flexibility of composing almost any pair of adjacent constitu- ents with a precise notion of syntactic grammatica- lity (Steedman, 1990; 1993). z The rest of the paper is organized as follows. First, we discuss in §2 how traditional techniques address availability of readings and note some residual pro- blems. Then we give a brief analysis of available readings (§3), a generalization of the analysis (§4), and finally describe a computational implementation in Prolog (~5). 2 Traditional Approaches All three …

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