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)

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].

We present Property Theory with Curry Typing (PTCT), an intensional first-order logic for natural language semantics. PTCT permits fine-grained specifications of meaning. It also supports polymorphic types and separation types. We develop an intensional number theory within PTCT in order to represent proportional generalized quantifiers like “most.” We use the type system and our treatment of generalized quantifiers in natural language to construct a type-theoretic approach to pronominal anaphora that avoids some of the difficulties that undermine previous type-theoretic analyses of (...) this phenomenon. (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)

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.

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)

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)