Quantifiers and Discourse Processing Kevin B. Paterson 1 *, Ruth Filik 2 and Linda M. Moxey 3 1 University of Leicester, 2 University of Nottingham and 3 University of Glasgow Abstract Quantifiers are ubiquitous in natural language and, in addition to providing information about quantity, they serve important discourse functions. We outline several theoretical accounts of the functions that quantifiers perform in a discourse and the factors governing their interpretation, focusing on two specific topics that have received substantial attention from researchers working in linguistics and psychology. The first topic concerns the interpretation of pronominal anaphora in different quantification contexts, and we review evidence showing that the focusing effects of positive and negative quantifiers license different patterns of pronominal reference. The second topic concerns the interpretation of quantifiers that function as anaphors in a discourse, and we consider recent experimental evidence in relation to two current and highly influential theories of semantic interpretation. Quantifiers are ubiquitous in natural language, and include expressions such as some, all, most, none, a few, few, a large number, a small proportion, lots, and a significant amount. The most obvious function of these expressions is to convey information about an amount or a proportion. However, as should become clear in this review, quantifiers have other characteristics, and serve important functions in discourse, that make them an important subject of linguistic and psychological research. Quantification is a central topic in formal semantics research (e.g., Montague 1973; Barwise and Cooper 1981; Kamp and Reyle 1993; Partee et al. 1993), which aims to provide an account of the syntax and semantics of natural language quantifiers using mathematical techniques drawn from formal logic and set theory. The approach is strongly influenced by a series of papers from the 1980s that provided a general mathe- matical framework for describing the properties of natural language quantifiers and that has since become known as Generalized Quantifier Theory (GQT; Barwise and Cooper 1981; van Benthem 1986; Keenan and Stavi 1986; see also Montague 1973). The aim of GQT was to provide a formal set-theoretic account of semantic properties that are uni- versal to natural language quantifiers. Such properties include conservativity, which requires that the truth of a quantified statement depends only on an evaluation of individuals denoted by its first argument (which is also called the domain of quantification). More simply, this means that to determine whether all of the students were at the lecture is true it is necessary to check only the location of the students and not, for example, the where- abouts of the professors. Another universal property of quantifiers that we will consider in more detail shortly is monotonicity, which refers to the patterns of logical inference licensed by different quantifiers. In contrast with the emphasis placed on quantification in formal semantics, there is much less research into quantification in psychology. Indeed, what psychological research exists has been concerned primarily with deductive reasoning (and for a review see, e.g., Johnson-Laird and Byrne 1991; but see also Geurts 2003a for an approach to syllogistic Language and Linguistics Compass 3/6 (2009): 1390–1402, 10.1111/j.1749-818x.2009.00166.x ª 2009 The Authors Journal Compilation ª 2009 Blackwell Publishing Ltd