I argues that quantificational adverbs are unselective binders over individuals. The Lewisian analysis, however, fails to recognize the ambiguity in some quantificationally modified conditionals. That the Lewisian approach cannot predict some attested reading is known as the “proportion problem.” I propose a solution based on the following ideas: (a) quantificational adverbs bind selectively; (b) a singular indefinite and its anaphoric pronoun may introduce a plural discourse referent, and (c) plural predication is elusive.

I survey the role of trivalence in theories of anaphora.

The meaning of definite descriptions (like ‘the King of France’, ‘the girl’, etc.) has been a central topic in philosophy and linguistics for the past century. Indefinites (‘Something is on the floor’, ‘A child sat down’, etc.) have been relatively neglected in philosophy, under the Russellian assumption that they can be unproblematically treated as existential quantifiers. However, an important tradition, drawing from Stoic logic, has pointed to patterns which suggest that indefinites cannot be treated simply as existential quantifiers. The standard (...) dynamic semantic treatment of those phenomena, however, has well-known problems with negation and disjunction. -/- In this paper I develop a new approach to (in)definites. On my theory, truth-conditions are classical. But in addition to truth-conditions, meanings comprise a second dimension of what I call bounds. It is at the level of bounds, not truth-conditions, that I locate the characteristically dynamic coordination between indefinites and definites. The resulting system thus has a classical logic. This approach avoids dynamic semantics’ logical problems, and, more generally, yields a new perspective on the relation between truth-conditional and dynamic effects in natural language. (shrink)

We propose a new approach to conditional donkey sentences that allows us to face successfully the often called proportion problem. The main ingredients of the proposal are van Benthem's generalized quantifier approach to conditionals, and Barwise's situation semantics. We present some experimental data supporting our proposal.

This book combines insights from philosophy and linguistics to develop a novel framework for theorizing about linguistic meaning and the role of context in interpretation. A key innovation is to introduce explicit representations of context — assignment variables — in the syntax and semantics of natural language. The proposed theory systematizes a spectrum of “shifting” phenomena in which the context relevant for interpreting certain expressions depends on features of the linguistic environment. Central applications include local and nonlocal contextual dependencies with (...) quantifiers, attitude ascriptions, conditionals, questions, and relativization. The result is an innovative, philosophically informed compositional semantics compatible with the truth-conditional paradigm. (shrink)

Donkey sentences have existential and universal readings, but they are not often perceived as ambiguous. We extend the pragmatic theory of nonmaximality in plural definites by Križ (2016) to explain how context disambiguates donkey sentences. We propose that the denotations of such sentences produce truth-value gaps — in certain scenarios the sentences are neither true nor false — and demonstrate that Križ’s pragmatic theory fills these gaps to generate the standard judgments of the literature. Building on Muskens’s (1996) Compositional Discourse (...) Representation Theory and on ideas from supervaluation semantics, the semantic analysis defines a general schema for quantification that delivers the required truth-value gaps. Given the independently motivated pragmatic theory of Križ 2016, we argue that mixed readings of donkey sentences require neither plural information states, contra Brasoveanu 2008, 2010, nor error states, contra Champollion 2016, nor singular donkey pronouns with plural referents, contra Krifka 1996, Yoon 1996. We also show that the pragmatic account improves over alternatives like Kanazawa 1994 that attribute the readings of donkey sentences to the monotonicity properties of the embedding quantifier. (shrink)

The paper argues that two distinct and independent notions of plurality are involved in natural language anaphora and quantification: plural reference (the usual non-atomic individuals) and plural discourse reference, i.e., reference to a quantificational dependency between sets of objects (e.g., atomic/non-atomic individuals) that is established and subsequently elaborated upon in discourse. Following van den Berg (PhD dissertation, University of Amsterdam, 1996), plural discourse reference is modeled as plural information states (i.e., as sets of variable assignments) in a new dynamic system (...) couched in classical type logic that extends Compositional DRT (Muskens, Linguistics and Philosophy, 19, 143-186, 1996). Given the underlying type logic, compositionality at sub-clausal level follows automatically and standard techniques from Montague semantics become available. The idea that plural info states are semantically necessary (in addition to non-atomic individuals) is motivated by relative-clause donkey sentences with multiple instances of singular donkey anaphora that have mixed (weak and strong) readings. At the same time, allowing for non-atomic individuals in addition to plural info states enables us to capture the intuitive parallels between singular and plural (donkey) anaphora, while deriving the incompatibility between singular (donkey) anaphora and collective predicates. The system also accounts for empirically unrelated phenomena, e.g., the uniqueness effects associated with singular (donkey) anaphora discussed in Kadmon (Linguistics and Philosophy, 13, 273-324, 1990) and Heim (Linguistics and Philosophy, 13, 131-177, 1990) among others. (shrink)

Unbound anaphoric pronouns or ‘E-type pronouns’ have presented notorious problems for semantic theory, leading to the development of dynamic semantics, where the primary function of a sentence is not considered that of expressing a proposition that may act as the object of propositional attitudes, but rather that of changing the current information state. The older, ‘E-type’ account of unbound anaphora leaves the traditional notion of proposition intact and takes the unbound anaphor to be replaced by a full NP whose semantics (...) is assumed to be known (e.g. a definite description). In this paper, I argue that there are serious problems with any version of the E-type account as well as the (original form of the) dynamic account. I will explore a new account based on structured propositions, which can be considered a conservative extension of a traditional proposition-based semantics, but which at the same time incorporates some crucial insights of the dynamic account. (shrink)

Ways of Scope Taking is concerned with syntactic, semantic and computational aspects of scope. Its starting point is the well-known but often neglected fact that different types of quantifiers interact differently with each other and other operators. The theoretical examination of significant bodies of data, both old and novel, leads to two central claims. (1) Scope is a by-product of a set of distinct Logical Form processes; each quantifier participates in those that suit its particular features. (2) Scope interaction is (...) further constrained by the semantics of the interacting operators. The arguments are developed using Minimalist syntax, Generalized Quantify theory, Discourse Representation Theory, and algebraic semantics. The contributors (Beghelli, Ben-Shalom, Doetjes, Farkas, Gutiérrez Rexach, Honcoop, Stabler, Stowell, Szabolcsi and Zwarts) make tightly related theoretical assumptions and focus on related empirical phenomena, which include the direct and inverse scope of quantifiers, distributivity, negation, modal and intensional contexts, weak islands, event-related readings, interrogatives, wh/quantifier interactions, and Hungarian syntax. An introduction to the formal semantics background is provided. Audience: Linguists, philosophers, computational and psycholinguists; advanced undergraduates, graduate students and researchers in these fields. (shrink)

In the semantics of natural language, quantification may have received more attention than any other subject, and one of the main topics in psychological studies on deductive reasoning is syllogistic inference, which is just a restricted form of reasoning with quantifiers. But thus far the semantical and psychological enterprises have remained disconnected. This paper aims to show how our understanding of syllogistic reasoning may benefit from semantical research on quantification. I present a very simple logic that pivots on the monotonicity (...) properties of quantified statements - properties that are known to be crucial not only to quantification but to a much wider range of semantical phenomena. This logic is shown to account for the experimental evidence available in the literature as well as for the data from a new experiment with cardinal quantifiers ("at least n" and "at most n"), which cannot be explained by any other theory of syllogistic reasoning. (shrink)

In this paper I present experimental data showing that the interpretation of donkey sentences is influenced by certain aspects of world knowledge that seem to elude introspective observation, which I try to explain by reference to a scale ranging from prototypical individuals (like children) to quite marginal ones (such as railway lines). This ontological cline interacts with the semantics of donkey sentences: as suggested already by the anecdotal data on which much of the literature is based, the effect of world (...) knowledge is by and large restricted to donkey sentences with non-intersective determiners. I outline a psychological model which incorporates both ontological and logical factors, and suggest that there may be something wrong with the standard assumption that a statement's receiving a truth value requires that it have a definite reading. (shrink)

This short paper describes a perspective on questions which does not view wh-words as existential quantifiers or as expressions introducing a quantificational domain, but rather as indeterminate referential expressions (Dotlačil and Roelofsen 2019). The proposal is programmatic in nature, and several aspects of it remain to be worked out in greater detail. I argue, however, that it has several potential benefits, including a principled account of weak and strong question interpretations, a uniform analysis of single-wh and multiple-wh questions, and an (...) account of the typologically widespread similarity between interrogative and indefinite pronouns which, unlike previous approaches, can explain the observation that if a language contains interrogative and indefinite pronouns which are similar in form but non-identical (e.g., where and somewhere), the indefinite pronouns are always morphologically more complex than the interrogative pronouns, and never the other way around (Haspelmath 1997). The tentative proposal is that an interrogative pronoun involves complete indeterminacy in the sense that it does not only leave open what its referential value is but also whether it has a referential value at all. For instance, where is completely indeterminate, permitting lack of a referential value. The ‘some’ in somewhere eliminates this possibility and thereby exerts existential force. (shrink)

So-called 'dynamic' semantic theories such as Kamp's discourse representation theory and Heim's file change semantics account for such phenomena as cross-sentential anaphora, donkey anaphora, and the novelty condition on indefinites, but compare unfavorably with Montague semantics in some important respects (clarity and simplicity of mathematical foundations, compositionality, handling of quantification and coordination). Preliminary efforts have been made by Muskens and by de Groote to revise and extend Montague semantics to cover dynamic phenomena. We present a new higher-order theory of discourse (...) semantics which improves on their accounts by incorporating a more articulated notion of context inspired by ideas due to David Lewis and to Craige Roberts. On our account, a context consists of a common ground of mutually accepted propositions together with a set of discourse referents preordered by relative salience. Employing a richer notion of contexts enables us to extend our coverage beyond pronominal anaphora to a wider range of presuppositional phenomena, such as the factivity of certain sentential-complement verbs, resolution of anaphora associated with arbitrarily complex definite descriptions, presupposition 'holes' such as negation, and the independence condition on the antecedents of conditionals. Formally, our theory is expressed within a higher-order logic with natural number type, separation-style subtyping, and dependent coproducts parameterized by the natural numbers. The system of semantic types builds on proposals due to Thomason and to Pollard in which the type of propositions (static meanings of sentential utterances) is taken as basic and worlds are constructed from propositions (rather than the other way around as in standard Montague semantics). (shrink)

Providing a compositional interpretation procedure for discourses in which descriptions of complex dependencies between interrelated objects are incrementally built is a key challenge for formal theories of natural language interpretation. This paper examines several quantificational phenomena and argues that to account for these phenomena, we need richly structured contexts of interpretation that are passed on between different parts of the same sentence and also across sentential boundaries. The main contribution of the paper is showing how we can add structure to (...) contexts in an incremental way, starting with the basic notion of context in classical first-order logic, i.e., interpretation contexts formalized as single total variable assignments. (shrink)

Quantifiers in Language and Logic (QLL) is a major contribution to natural language semantics, specifically to quantification. It integrates the extensive recent work on quantifiers in logic and linguistics. It also presents new observations and results. QLL should help linguists understand the mathematical generalizations we can make about natural language quantification, and it should interest logicians by presenting an extensive array of quantifiers that lie beyond the pale of classical logic. Here we focus on those aspects of QLL we judge (...) to be of specific interest to linguists, and we contribute a few musings of our own, as one mark of a worthy publication is whether it stimulates the reader to seek out new observations, and QLL does. QLL is long and fairly dense, so we make no attempt to cover all the points it makes. But QLL has a topic index, a special symbols index and two tables of contents, a detailed one and an overview one, all of which help make it user friendly. QLL is presented in four parts: I, "The Logical Conception of Quantifiers and Quantification" with an introductory section "Quantification". II, "Quantifiers of Natural Language", the most extensive section in the book and of the most direct interest to linguists. III, "Beginnings of a Theory of Expressiveness, Translation, and Formalization" introduces notions of expressive power and definability, and IV, presents recent work and techniques concerning quantifier definability over finite domains, making accessible to linguists recent work in finite model theory. (shrink)

This paper explores the idea that scalar implicatures are computed with respect todiscourse referents. Given the general consensus that a proper account of pronominal anaphora in natural language requires discourse referents separately from the truth-conditional meaning, it is naturally expected that the anaphoric information that discourse referents carry play a role in the computation of scalar implicatures, but the literature has so far mostly exclusively focused on the truth-conditional dimension of meaning. This paper offers a formal theory of scalar implicatures (...) with discourse referents couched in dynamic semantics, and demonstrates its usefulness through a case study on the plurality inferences of plural nouns in English. (shrink)

Approaches to anaphora generally seek to explain the potential for a DP to covary with a pronoun in terms of a combination of factors, such as the inherent semantics of the antecedent DP, its scope properties, and its structural position. A case in point is Reinhart’s classic condition on bound anaphora, paraphrasable as A DP can antecede a pronoun pro only if the DP c-commands pro at S-structure, supplemented with some extra machinery to allow indefinites to covary with pronouns beyond (...) their c-command domains. In the present paper, I explore a different take. I propose that anaphora is governed not by DPs and their properties; it is governed by predicates and their properties. To use a metaphor from dynamic semantics: discourse referents can only be ‘activated’ by predicates, never by DPs. This conceptually simple assumption is shown to have far-reaching consequences. For one, it yields a new take on weak crossover, arguably worthy of consideration. Moreover, it leads to a further general “restatement of the anaphora question”, in Reinhart’s words. (shrink)

Linguists often sharply distinguish the different modules that support linguistics competence, e.g., syntax, semantics, pragmatics. However, recent work has identified phenomena in syntax (polarity sensitivity) and pragmatics (implicatures), which seem to rely on semantic properties (monotonicity). We propose to investigate these phenomena and their connections as a window into the modularity of our linguistic knowledge. We conducted a series of experiments to gather the relevant syntactic, semantic and pragmatic judgments within a single paradigm. The comparison between these quantitative data leads (...) us to four main results, (i) Our results support a departure from one element of the classical Gricean approach, thus helping to clarify and settle an empirical debate. This first outcome also confirms the soundness of the methodology, as the results align with standard contemporary accounts of scalar implicature (SI), (ii) We confirm that the formal semantic notion of monotonicity underlies negative polarity item (NPI) syntactic acceptability, but (iii) our results indicate that the notion needed is perceived monotonicity. We see results (ii) and (iii) as the main contribution of this study: (ii) provides an empirical interpretation and confirmation of one of the insights of the model-theoretic approach to semantics, while (iii) calls for an incremental, cognitive implementation of the current generalizations, (iv) Finally, our results do not indicate that the relationship between NPI acceptability and monotonicity is mediated by pragmatic features related to Sis: this tells against elegant attempts to unify polarity sensitivity and Sis (pioneered by Krifka and Chierchia). These results illustrate a new methodology for integrating theoretically rigorous work in formal semantics with an experimentally-grounded cognitively-oriented view of linguistic competence. (shrink)

Conservativity in generalized quantifiers is linked to presupposition filtering, under a propositions-as-types analysis extended with dependent quantifiers. That analysis is underpinned by modeltheoretically interpretable proofs which inhabit propositions they prove, thereby providing objects for quantification and hooks for anaphora.

With this paper I aim to demonstrate that a look beyond the Aristotelian square of opposition, and a related non-conservative view on logical determiners, contributes to both the understanding of Aristotelian syllogistics as well as to the study of quantificational structures in natural language.

Donkey pronouns (e.g., it in Every farmer who owns a donkey beats it) are argued to have an interpretation more similar to a demonstrative phrase (e.g., . . . beats that donkey) than to any of the other alternatives generally considered (e.g., . . . the donkey(s) he owns, . . . a donkey he owns). Like the demonstrative phrase, the pronoun is not equivalent to Evans' E-type paraphrase, nor to either the weak or the strong reading sometimes claimed for (...) donkey sentences. A consequence is to narrow the range of formal analyses. (shrink)

Proceedings of the 11th Semantics and Linguistic Theory Conference, held May 11-13, 2001, at New York University.

We give a condensed survey of recent research on generalized quantifiers in logic, linguistics and computer science, under the following headings: Logical definability and expressive power, Polyadic quantifiers and linguistic definability, Weak semantics and axiomatizability, Computational semantics, Quantifiers in dynamic settings, Quantifiers and modal logic, Proof theory of generalized quantifiers.

This paper introduces an interesting class of predicates that come in pairs, so-called total and partial predicates. It will be shown that such predicates contribute to an explanation for the weak and strong interpretations of donkey sentences. This paper proposes that the phenomenon of weak and strong interpretations is real, and that whether a sentence receives the weak or the strong interpretation depends on the predicate in the nuclear scope of the sentence. It also proposes that sum individuals are calculated (...) at some level before the nuclear scope of the sentence is processed. Once the sum individuals are calculated, it will be decided whether the nuclear scope is true of at least one element of the sum individual (weak interpretation) or true of all elements of the sum individual (strong interpretation). (shrink)

Research in dynamic semantics has made strides by studying various aspects of discourse in terms of computational effect systems, for example, monads (Shan, 2002; Charlow, 2014), Barker and 2014), (Maršik, 2016). We provide a system, based on graded monads, that synthesizes insights from these programs by formalizing individual discourse phenomena in terms of separate effects, or grades. Included are effects for introducing and retrieving discourse referents, non-determinism for indefiniteness, and generalized quantifier meanings. We formalize the behavior of individual effects, as (...) well as the interactions between effects, in terms of algebraic laws tailored to the relevant discourse phenomena. The system we propose is thus modular and suggests a novel approach to integrating formal accounts of distinct semantic phenomena. Finally, we give an interpretation of the system into pure \( \lambda \) -calculus that respects the laws. Future work will aim to integrate more discourse phenomena using the same methodology, for example, presupposition and conventional implicature. (shrink)

I argue that common nouns should be analyzed as variables, rather than as predicates which take variables as arguments. This necessitates several unusual features to the analysis, such as allowing variables to be modally non-rigid, and assigning their values compositionally. However, treating common nouns as variables offers a variety of theoretical and empirical advantages over a more traditional analysis: It predicts the conservativity of nominal quantification, simplifies the analysis of articleless languages, derives the weak reading of sentences with donkey anaphora, (...) solves the proportion problem presented by quantifiers like ‘most’, improves the analysis of the temperature paradox, allows a more unified analysis of bare plurals, and regularizes the correspondence between syntactic categories and semantic types. (shrink)

It is generally agreed that some anaphoric pronouns with quantifier antecedents occur outside the syntactic scope of their antecedents. First, there is “donkey anaphora,” of both the conditional and relative clause varieties:If Sarah owns a donkey, she beats it.Every woman who owns a donkey beats it.Without going through the details, let me just assert that there is good reason to think that the pronouns in and do not occur in the syntactic scope of the quantifier’ a donkey’. A second sort (...) of case in which a pronoun with a quantified antecedent occurs outside the syntactic scope of its quantifier antecedent is one in which the pronoun and its antecedent occur in different sentences.A second sort of case in which a pronoun with a quantified antecedent occurs outside the syntactic scope of its quantifier antecedent is one in which the pronoun and its antecedent occur in different sentences. Examples of such “discourse anaphora,” from the very simple to the slightly complex, include:A man is following Sarah. He is from the Internal Revenue Service.A man is following Sarah. Melanie believes he is from the Internal Revenue Service.It is possible that several students flunked at most five exams. Melanie believes they didn’t study for them.Suzi ought to apologize to most of Ann’s dinner guests. It is certain that she insulted them. But it is unclear whether they noticed. (shrink)

Most studies of the so-called proportion problem seek to understand how lexical and structural properties of sentences containing adverbial quantifiers give rise to various proportional readings. This paper explores a related but distinct problem: given a use of a particular sentence in context, why do only some of the expected proportional readings seem to be available? That is, why do some sentences allow an asymmetric reading when other, structurally similar sentences seem to require a symmetric reading? Potential factors suggested in (...) the literature include the distribution of donkey pronouns, certain uniqueness implications, and focus structures. I argue here that the use of an adverbial quantifier presupposes HOMOGENEITY: all individual situations that get lumped into a single case for the purposes of evaluating the quantification must agree on whether they satisfy the nuclear scope. For instance, in order for a token of Usually, if a farmer owns a donkey, he beats it to be felicitous when construed under a farmer-dominant asymmetric reading, the context must be consistent with the proposition that each farmer either beats all or none of his donkeys. Thus proportional sentences are indeed systematically ambiguous, but only some readings will be felicitous in a given context. (shrink)

The paper proposes a novel analysis of quantificational subordination, e.g. Harvey courts a woman at every convention. {She is very pretty. vs. She always comes to the banquet with him.} (Karttunen 1976), in particular of the fact that the indefinite in the initial sentence can have wide or narrow scope, but the first discourse as a whole allows only for the wide scope reading, while the second discourse allows for both readings. The cross-sentential interaction between scope and anaphora is captured (...) in terms of structured anaphora to quantifier domains, formalized in a new dynamic system couched in classical type logic; given the underlying type logic, Montague-style compositionality at sub-clausal level follows automatically. Modal subordination (Roberts 1987) is analyzed in a parallel way, thereby capturing the parallels between the individual and modal domains argued for in Stone (1999). Several other phenomena are analyzed in terms of structured anaphora: exceptional wide scope, weak / strong donkey readings, anaphoric / uniqueness-implying definite descriptions and interactions between same / different and quantifier scope. (shrink)