Quantification is a topic which brings together linguistics, logic, and philosophy. Quantifiers are the essential tools with which, in language or logic, we refer to quantity of things or amount of stuff. In English they include such expressions as no, some, all, both, many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role.

This is the first part of a two-part article on semantic compositionality, that is, the principle that the meaning of a complex expression is determined by the meanings of its parts and the way they are put together. Here we provide a brief historical background, a formal framework for syntax and semantics, precise definitions, and a survey of variants of compositionality. Stronger and weaker forms are distinguished, as well as generalized forms that cover extra-linguistic context dependence as well as linguistic (...) context dependence. In the second article, we survey arguments for and arguments against the claim that natural languages are compositional, and consider some problem cases. It will be referred to as Part II. (shrink)

In this paper, I have proposed a compositional semantic analysis of exception NPs from which three core properties of exception constructions could be derived. I have shown that this analysis overcomes various empirical and conceptual shortcomings of prior proposals of the semantics of exception sentences. The analysis was first formulated for simple exception NPs, where the EP-complement was considered a set-denoting term and the EP-associate was a monadic quantifier. It was then generalized in two steps: first, in order to account (...) for quantified EP-complements, and second, in order to account for polyadic quantifiers as the EP-associates. An additional assumption that was made in several places was that EPs may operate at the level of implications. The consequences of this assumption, though, still have to be investigated. (shrink)

It is argued that the English bare plural (an NP with plural head that lacks a determiner), in spite of its apparently diverse possibilities of interpretation, is optimally represented in the grammar as a unified phenomenon. The chief distinction to be dealt with is that between the generic use of the bare plural (as in Dogs bark) and its existential or indefinite plural use (as in He threw oranges at Alice). The difference between these uses is not to be accounted (...) for by an ambiguity in the NP itself, but rather by explicating how the context of the sentence acts on the bare plural to give rise to this distinction. A brief analysis is sketched in which bare plurals are treated in all instances as proper names of kinds of things. A subsidiary argument is that the null determiner is not to be regarded as the plural of the indefinite article a. (shrink)

Precursors. 2.1 Introduction Thus far I have presented an approach to the semantics of plurals in the form of two rather similar grammars for a fragment of English. And I have given a few examples of the kinds of things one can say within this ...

This note explains the circumstances under which a type 1 quantifier can be decomposed into a type 1, 1 quantifier and a set, by fixing the first argument of the former to the latter. The motivation comes from the semantics of Noun Phrases (also called Determiner Phrases) in natural languages, but in this article, I focus on the logical facts. However, my examples are taken among quantifiers appearing in natural languages, and at the end, I sketch two more principled linguistic (...) applications. (shrink)

For the first time a uniform compositional derivation is given for quantified sentences containing exceptive constructions. The semantics of exceptives is primarily one of subtraction from the domain of a quantifier. The crucial semantic difference between the highly grammaticized but-phrases and free exceptives is that the former have the Uniqueness Condition as part of their lexical meaning whereas the latter are mere set subtractors. Several empirical differences between the two types of exceptives are shown to follow from this basic lexical (...) difference. (shrink)

This dissertation investigates the ways in which natural language restricts the domains of quantifiers. Adverbs of quantification are analyzed as quantifying over situations. The domain of quantifiers is pragmatically constrained: apparent processes of "semantic partition" are treated as pragmatic epiphenomena. The introductory Chapter 1 sketches some of the background of work on natural language quantification and begins the analysis of adverbial quantification over situations. Chapter 2 develops the central picture of "semantic partition" as a side-effect of pragmatic processes of anaphora (...) resolution. I argue that the apparent effects of topic/focus articulation and presuppositional information on the interpretation of quantifiers are not the result of a direct and local mechanism of sentence grammar. Instead, I develop an analysis where the link is established via the anaphoric dependence of quantifier domains on the discourse context. Chapter 3 discusses the analysis of conditional clauses as quantifier restrictors, concentrating on the question whether conditional clauses restrict quantifiers directly or indirectly. A treatment is explored which has if-clauses constrain the value of the hidden domain variable of the restricted quantifier. Chapter 4, on unless-clauses, and Chapter 5, on only if- and even if-clauses, present some issues in the compositional analysis of complex conditional clauses. These chapters significantly expand the data coverage of the theory of A-quantification. Building on previous work of mine on exceptives, I analyze unless-clauses as exceptive operators on A-quantifiers. The analysis of only if-clauses, treated as conditional clauses that combine if with the focus adverb only, unearthes some interesting new properties. Chapter 6, finally, examines the phenomenon of donkey-anaphora in the light of the results of the previous chapters. I show that a solution to the proportion problem may become possible once we combine the situation-semantic approach to adverbial quantification with the pragmatic theory developed in Chapter 2 and further elaborated in the analysis of donkey anaphora in complex conditionals. (shrink)

This paper begins with a discussion ofcumulativity (e.g., ‘P(a) & P(b) implies P(a+b)’), formalized using a verb phrase operator. Next, the meanings of distributivity markers such aseach and non-distributivity indicators such astogether are considered. An existing analysis ofeach in terms of quantification over parts of a plurality is adopted. However,together is problematic, for it involves a cancellation or negation of the quantification associated witheach. (The four boys together owned exactly three cars could not be true if each of the boys (...) owned three cars, though the same sentence withouttogether could be.) A refinement of this idea of negated quantification over parts is proposed as an analysis for non-distributivity operators. It is then worked out in the system described in Cooper (1983), in which positive and negative extensions are assigned. Presuppositions connected with plural reference are considered at this point as well. Finally, the cumulativity operator is argued to be quantificational and therefore sensitive to contextual domain selection. This context sensitivity is claimed to be the source of distributive readings that appear in the absence of modifiers likeeach and non-distributive or collective readings that arise withouttogether. (shrink)

It is generally assumed that there are two types of genericity, called characterizing statements and kind reference in Krifka et al. (1995). Characterizing statements express generalizations about sets of entities or situations, cf. (1); kind reference involves reference to an entity that is related to specimens, cf. (2).

This paper addresses two puzzles in the semantics of connected exceptive phrases (EP): (i) the compatibility of EPs modifying noun phrases headed by the negative polarity item (NPI) determiner any and (ii) the ability of a negative universal quantifier modified by an EP to license strong NPIs. Previous analyses of EPs are shown to fail to solve these puzzles. A new unified solution to the two puzzles is proposed. The crucial insight of the analysis is to allow von Fintel’s (Natural (...) Language Semantics 1: 123–148, 1993; Restrictions on quantifier domains, PhD dissertation, 1994) leastness condition on EPs to be imposed at scopes non-local to the surface position of the EP. A general result is derived concerning the truth conditions of sentences in which an existential modified by an EP occurs in the scope of a downward entailing operator. The distribution of EPs is argued to depend on how the leastness condition interacts with other pragmatic strengthening conditions, such as the one imposed on any by Kadmon and Landman (Linguistics and Philosophy 16: 353–422, 1993). (shrink)