This article focuses on foundational issues in dynamic and static semantics, specifically on what is conceptually at stake between the dynamic framework and the truth-conditional framework, and consequently what kinds of evidence support each framework. The article examines two questions. First, it explores the consequences of taking the proposition as central semantic notion as characteristic of static semantics, and argues that this is not as limiting in accounting for discourse dynamics as many think. Specifically, it explores what it means for (...) a static semantics to incorporate the notion of context change potential in a dynamic pragmatics and denies that this conception of static semantics requires that all updates to the context be eliminative and distributive. Second, it argues that the central difference between the two frameworks is whether semantics or pragmatics accounts for dynamics, and explores what this means for the oft-heard claim that dynamic semantics blurs the semantics/pragmatics distinction. (shrink)

Noun phrases with overt determiners, such as <i>some apples</i> or <i>a quantity of milk</i>, differ from bare noun phrases like <i>apples</i> or <i>milk</i> in their contribution to aspectual composition. While this has been attributed to syntactic or algebraic properties of these noun phrases, such accounts have explanatory shortcomings. We suggest instead that the relevant property that distinguishes between the two classes of noun phrases derives from two modes of existential quantification, one of which holds the values of a variable fixed (...) throughout a quantificational context while the other allows them to vary. Inspired by Dynamic Plural Logic and Dependence Logic, we propose Plural Predicate Logic as an extension of Predicate Logic to formalize this difference. We suggest that temporal <i>for</i>-adverbials are sensitive to aspect because of the way they manipulate quantificational contexts, and that analogous manipulations occur with spatial <i>for</i>-adverbials, habituals, and the quantifier <i>all</i>. (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)

This paper proposes a semantics for free choice permission that explains both the non-classical behavior of modals and disjunction in sentences used to grant permission, and their classical behavior under negation. It also explains why permissions can expire when new information comes in and why free choice arises even when modals scope under disjunction. On the proposed approach, deontic modals update preference orderings, and connectives operate on these updates rather than propositions. The success of this approach stems from its capacity (...) to capture the difference between expressing the preferences that give rise to permissions and conveying propositions about those preferences. (shrink)

Brasoveanu (Linguist Philos 34:93–168, 2011) argues that “different” exhibits what he calls association with distributivity: a distributive operator such as “each” creates a two-part context that propagates through the compositional semantics in a way that can be accessed by a subordinate “different”. We show that Brasoveanu’s analysis systematically undergenerates, failing to provide interpretations of sentences such as “Every1 boy claimed every girl read a different1 poem”, in which “different” can associate with a non-local distributive operator. We provide a generalized version (...) of association with distributivity, implemented using de Groote’s (in: Proceedings of semantics and linguistic theory XVI, 2006) continuation-based dynamic semantics. We compare our analysis with the one in Brasoveanu (2011), drawing conclusions about computational tractability, scope of indefinites, and whether it is possible or even desirable to arrive at a unified analysis of internal and external readings of “different”. (shrink)

There are two main approaches to the problem of donkey anaphora (e.g. If John owns a donkey , he beats it ). Proponents of dynamic approaches take the pronoun to be a logical variable, but they revise the semantics of quantifiers so as to allow them to bind variables that are not within their syntactic scope. Older dynamic approaches took this measure to apply solely to existential quantifiers; recent dynamic approaches have extended it to all quantifiers. By contrast, proponents of (...) E-type analyses take the pronoun to have the semantics of a definite description (with it ≈ the donkey, or the donkey that John owns ). While competing accounts make very different claims about the patterns of coindexation that are found in the syntax, these are not morphologically realized in spoken languages. But they are in sign language, namely through locus assignment and pointing. We make two main claims on the basis of ASL and LSF data. First, sign language data favor dynamic over E-type theories: in those cases in which the two approaches make conflicting predictions about possible patterns of coindexation, dynamic analyses are at an advantage. Second, among dynamic theories, sign language data favor recent ones because the very same formal mechanism is used irrespective of the indefinite or non-indefinite nature of the antecedent. Going beyond this debate, we argue that dynamic theories should allow pronouns to be bound across negative expressions, as long as the pronoun is presupposed to have a non-empty denotation. Finally, an appendix displays and explains subtle differences between overt sign language pronouns and all other pronouns in examples involving ‘disjunctive antecedents’, and suggests that counterparts of sign language loci might be found in spoken language. (shrink)

The paper proposes the first unified account of deictic/sentence-external and sentence-internal readings of singular different . The empirical motivation for such an account is provided by a cross-linguistic survey and an analysis of the differences in distribution and interpretation between singular different , plural different and same (singular or plural) in English. The main proposal is that distributive quantification temporarily makes available two discourse referents within its nuclear scope, the values of which are required by sentence-internal uses of singular different (...) to be distinct, much as its deictic uses require the values of two discourse referents to be distinct. Thus, we take sentence-internal readings to be a form of ‘association with distributivity’ that is similar to association with focus. The contrast between singular different , plural different and same is explained in terms of several kinds of quantificational distributors that license their internal readings. The analysis is executed in a stack-based dynamic system couched in type logic, so we get compositionality in the usual Montagovian way. Quantificational subordination and dependent indefinites in various languages provide additional motivation for the account. Investigating the connections between items with sentence-internal readings and the quantificational licensors of these readings opens up a larger project of formally investigating (i) the typology of quantificational distributors and distributivity-dependent items and (ii) the fine-grained contexts of evaluation needed to capture this typological variation. (shrink)

The paper focuses on the semantics of distributivity, grammatical number, and cardinality predicates. I argue that constructions involving so-called ‘dependent plurals’, i.e. plurals lacking cardinality predicates occurring in the scope of certain quantificational items such as all and most, pose a challenge to familiar semantic frameworks that distinguish between two sources of multiplicity: mereological plurality and distributive quantification. I argue that dependent plural readings should be analysed as distinct both from cumulative readings and distributive readings, in the classical sense. I (...) demonstrate how this can be accomplished in a semantic framework where expressions are evaluated relative to sets of assignments, or plural info states Proceedings of the 7th Amsterdam Colloquium, ILLC, University of Amsterdam, Amsterdam, 1990, in Dekker and Stokhof Proceedings of the 9th Amsterdam Colloquium, ILLC, University of Amsterdam, Amsterdam, 1994, Some aspects of the Internal Structure of Discourse. The Dynamics of Nominal Anaphora. PhD thesis, University of Amsterdam, 1996). The specific formal implementation is based on a modified version of Brasoveanu’s :129–209. https://doi.org/10.1007/s10988-008-9035-0, 2008) Plural Compositional DRT. In this framework we are able to distinguish between two types of distributivity: weak distributivity across the assignments in a single plural info state and strong distributivity across multiple info states. I argue that both of these types of distributivity play a role in the semantics of natural language, accounting for the contrasting properties of ‘singular quantifiers’, such as each and every, and ‘plural quantifiers’, such as all and most. The contrasting properties of bare plurals and plurals involving cardinality modifiers are analysed in terms of the distinction between state-level and assignment-level plurality. (shrink)

Concord describes a natural language phenomenon in which a single logical meaning is expressed syntactically on multiple lexical items. The canonical example is negative concord, in which multiple negative expressions are used, but a single negation is interpreted. Formally similar phenomena have been observed for the redundant marking of distributivity and definiteness. Inspired by recent dynamic analyses of these latter two phenomena, we extend a similar dynamic analysis to negative concord. We propose that negative concord items introduce a discourse referent, (...) but then test that no discourse referent has been introduced in any assignment. These apparently contradictory requirements are licensed with split scope around negation: introduction occurs below negation; the test appears above it. The analysis successfully predicts that negative concord items must be licensed by a sufficiently local negative operator. We further show that modulation of what is at-issue can account for cases in which NC items themselves carry negative force. (shrink)

The paper proposes a novel solution to the problem of scope posed by natural language indefinites that captures both the difference in scopal freedom between indefinites and bona fide quantifiers and the syntactic sensitivity that the scope of indefinites does nevertheless exhibit. Following the main insight of choice functional approaches, we connect the special scopal properties of indefinites to the fact that their semantics can be stated in terms of choosing a suitable witness. This is in contrast to bona fide (...) quantifiers, the semantics of which crucially involves relations between sets of entities. We provide empirical arguments that this insight should not be captured by adding choice/Skolem functions to classical first-order logic, but in a semantics that follows Independence-Friendly Logic, in which scopal relations involving existentials are part of the recursive definition of truth and satisfaction. These scopal relations are resolved automatically as part of the interpretation of existentials. Additional support for this approach is provided by dependent indefinites, a cross-linguistically common class of special indefinites that can be straightforwardly analyzed in our semantic framework. (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)

In languages like English, reflexivity and reciprocity are expressed by distinct proforms. However, many languages, such as Cheyenne, express reflexivity and reciprocity with a single proform. In this paper I utilize Dynamic Plural Logic (van den Berg, 1996) to a draw a semantic parallel between reflexive and reciprocal anaphors in English. I propose that they contribute overlapping but distinct requirements on the relations introduced by transitive verbs, requirements which fully specify reflexivity and reciprocity. This parallel is then extended to Cheyenne (...) by appealing to underspecification. I propose the Cheyenne affix which expresses both reflexivity and reciprocity contributes only the shared requirement of the English anaphors. It is thus underspecified, not ambiguous. This accounts for its compatibility with both singular and plural antecedents as well as its variety of construals. (shrink)

The paper proposes a new semantics with dependent types for indefinites, encompassing both the data related to their exceptional scopal behavior and the data related to their anaphoric properties. The proposal builds on the formal system combining generalized quantifiers with dependent types in [Grudzińska & Zawadowski 2014] and [Grudzińska & Zawadowski 2016].

Quantifiers in phrasal and clausal comparatives often seem to take distributive scope in the matrix clause: for instance, the sentence John is taller than every girl is is true iff for every girl it holds that John is taller than that girl. Broadly speaking, two approaches exist that derive this reading without postulating the wide scope of the quantifier: the negation analysis and the interval analysis of than-clauses. We propose a modification of the interval analysis in which than-clauses are not (...) treated as degree intervals but as degree pluralities. This small change has significant consequences: it yields a straightforward account of differentials in comparatives and it correctly predicts the existence of hitherto unnoticed readings, viz. cumulative readings of clausal comparatives. Finally, this paper also makes the case that using degree pluralities is conceptually appealing: it allows us to restrict the analysis of comparatives by mechanisms that are postulated independently in the semantics of pluralities. (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)

A number of natural language constructions seem to provide access to structured pluralities — that is, pluralities of pluralities. A body of semantic work has debated how to model this additional structure and the extent to which it depends on pragmatics. In this article, after controlling for the distinction between ambiguity and underspecification, we present new data showing that structured pluralities are sometimes but not always available, depending on the form of the plural noun phrase used. We show that these (...) results challenge two longstanding theories of plurality. We sketch two different ways to account for these data and describe some of the diverging predictions they make. (shrink)