This paper introduces a novel approach to the semantics of plurals that is not based on the traditional distributive/collective distinction between predicates. Rather, the semantic number of nouns, verbs and adjectives is classified according to their behaviour under replacement of a plural determiner (e.g. all, plural no) by its singular counterpart (e.g. every, singular no). It is proposed that predicates that are insensitive to this replacement range over atomic entities, whereas number sensitive predicates range over sets of such atoms. This modeltheoretic property, together with morpho-syntactic number of predicates and the quantificational/non-quantificational distinction between noun phrases, governs the availability of collective interpretations. The emerging system offers a general solution to some long-standing problems concerning the differences between every, all and simple plural definites. 1 Introduction In a widely cited work, Vendler (1967:70-76) points ou...

Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, in a light example-based manner, where this elegant logical paradigm stands when confronted with the wear and tear of reality. Starting from a brief history of the Lambek tradition since the 1980s, we discuss three main issues: (a) the fit of the lambda calculus engine to characteristic semantic structures in natural language, (b) the coexistence of the original type-theoretic and more recent modal interpretations of categorial logics, and (c) the place of categorial grammars in the complex total architecture of natural language, which involves - amongst others - mixtures of interpretation and inference.

This article studies the monotonicity behavior of plural determiners that quantify over collections. Following previous work, we describe the collective interpretation of determiners such as all, some and most using generalized quantifiers of a higher type that are obtained systematically by applying a type shifting operator to the standard meanings of determiners in Generalized Quantifier Theory. Two processes of counting and existential quantification that appear with plural quantifiers are unified into a single determiner fitting operator, which, unlike previous proposals, both captures existential quantification with plural determiners and respects their monotonicity properties. However, some previously unnoticed facts indicate that monotonicity of plural determiners is not always preserved when they apply to collective predicates. We show that the proposed operator describes this behavior correctly, and characterize the monotonicity of the collective determiners it derives. It is proved that determiner fitting always preserves monotonicity properties of determiners in their second argument, but monotonicity in the first argument of a determiner is preserved if and only if it is monotonic in the same direction in the second argument. We argue that this asymmetry follows from the conservativity of generalized quantifiers in natural language.

this paper, we will consider sentences like (1) and (2) from the point of view of quantification and predication. Three girls mailed a letter (1) Three girls mailed four letters (2) As to the issue of quantification, Verkuyl & Van der Does 1991 tried to reduce the large numbers of readings often assigned to these sentences to just one by adopting a so-called scalar approach. This approach is based on the following observation. Scha 1981 stipulated that NPs are ambiguous between a distributive (D) reading and two collective readings (C 1 and C 2 ). In sentences with two NPs, combinations of these three readings lead to at least nine readings for (2): DD, DC 1 , : : :, C 2 C 2 . For example, on the DD-reading of (2), each of the girls mailed four letters, each letter on a different occasion. On the C 1 C 1 -reading, the girls mailed the four letters together on one occasion. The C 1 C 2 -reading would say that the three girls as a group mailed four letters, say on one occasion one letter, and one day later the three other letters. Observe that C 2 allows both 1+3- and 2+2-configurations of the set of four letters. In fact it also comprises D and C 1 . On the C 1 C 2 - reading just mentioned, C 2 allows also the 4- and the 1+1+1+1-configuration. Here the idea of a scale comes up quite naturally, but this idea was not taken up by Scha himself, nor did Link 1984 pay attention to it. Verkuyl & Van der Does 1991 decided to take a strengthening of the C 2 -reading as basic, in fact as the only reading that can be attached to (1) and (2). They chose (3) as the format for the analysis of the denotation of NPs like three girls in sentences such as (1) and (2):

In this article we study the interpretation of nominal anaphora by means of generalized quantifier theory. One way of viewing first-order DRT and DPL is that they interpret singular anaphora outside the scope of their antecedent by extending the antecedent's scope. Moving to the general case, we therefore want to know how general these scope principles are. We shall argue that they can be sustained for all singular anaphora, but that they may fail for plural anaphoric noun phrases. Some recent dynamic semantics of quantifiers are reviewed in this light. Our own proposal stands in the E-type tradition. It treats the relevant anaphora as generalized quantifiers which are contextually restricted by material inherited from their antecedent. Indeed, all E-type anaphora are interpreted by one and the same mechanism. To make this precise, we present a labelled, many dimensional categorial system, which generates the meaning of a wide class of discourses in a compositional way. 1 Introduction...

Abstract: Singular indefinite NPs in prevention statements give rise to an ambiguity between a general and a specific reading. In order to account for this ambiguity, we extend Zimmermann’s proposal for referential concept NPs to also allow for quantificational concept NPs. We further motivate the need for quantificational concept NPs on the basis of the interpretation of indefinite NPs with numeral determiners in prevention contexts. We treat numerals as generalized determiners quantifying over concepts and propose a way of counting concepts by counting maximally specific instantiated concepts. ✷ In [2] we argued that the object argument of prevent must be concept denoting rather than individual denoting. The singular indefinite NP a strike in (1) existentially quantifies over sub-concepts of the concept Strike, including the concept Strike itself. (1) Negotiations prevented a strike. (1) entails that Strike or some sub-concept of it is uninstantiated in the actual world, where negotiations occur. But in a counterfactual world, identical apart from the absence of negotiations, the concept is instantiated.

This paper focuses on problems concerning existence that arise specifically with prevent statements. Going beyond the treatments of nondenoting names recently discussed in [4], we hope to sharpen the requirements for a general treatment of existence in knowledge representation and natural language semantics

Abstract not found

Reciprocal expressions like each other and one another introduce some well-known challenges for logical semantic theories. One central problem concerns the variety of interpretations

Reciprocal expressions like each other and one another introduce some well-known challenges for logical semantic theories. One central problem concerns the variety of interpretations