This paper presents a generalization of the standard notions of left monotonicity (on the nominal argument of a determiner) and right monotonicity (on the VP argument of a determiner). Determiners such as “more than/at least as many as” or “fewer than/at most as many as”, which occur in so-called propositional comparison, are shown to be monotone with respect to two nominal arguments and two VP-arguments. In addition, it is argued that the standard Generalized Quantifier analysis of numerical determiners such as (...) “more than three/at least three” is a simplification which ignores the fundamental parallellism with the propositional comparatives. Furthermore, the symmetric monotonicity configurations of the existential “some” and “no” are shown to be straightforwardly related to those of numerical comparatives with the limit numeral zero, whereas the asymmetric configurations of universal “all” and “not all” involve the extra complicating mechanism of polarity reversal, which is related to Keenan's notion of co-intersectivity (as opposed to intersectivity). A second aim of the paper is to investigate some of the factors reducing the inferential potential of determiners. Different types of comparative determiners and their modification will be considered in detail. In addition, a systematic interaction will be revealed between the monotonicity properties of the determiners in propositional comparatives and the differ ent types of ellipsis in the “than”-complement. Different degrees of ellipsis are defined in terms of informational dependencies between the “than”-complement and the main clause. A general balancing mechanism is observed by virtue of which an increase in informational dependency is compensated by a reduction of the inferential potential of the comparative determiner. The structure of the paper is as follows. Part two deals with propositional comparison and introduces the two basic monotonicity configurations. Part three distinguishes three types of informational dependencies or ellipsis between the “than”-complement and the main clause. In Section 3.1 the “than”-complement only contains a VP constituent, whereas in Section 3.2. it only consists of a nominal constituent. Section 3.3 considers more complex instances of multiple dependencies. Section 3.4 then looks at the interaction of these three types with the modifier “proportionally”. Part four presents the two basic monotonicity configurations for numerical comparison, whereas part five deals with more complex numerical determiners. Bounding determiners, such as “between five and ten”, and other boolean combinations are discussed in Section 5.1, whereas Section 5.2 goes into approximative determiners involving modifiers such as “only” or “almost”. Section 5.3. is devoted to proportional determiners such as “more than two out of three”. Part six then considers the standard existential and universal quantifiers. Section 6.1 reformulates the standard Generalized Quantifier analysis in comparative terms, whereas Section 6.2 deals with exception determiners of the form “all but five”. (shrink)

Argues for an assimilation of sentential and predicate conjunction to collective conjunction, based on modification of predicates by adverbs such as 'alternately'.

This paper discusses Japanese numeral quantifiers that are used to count individuals, rather than quantities, of a substance, and which may occur either as floated or non-floated quantifiers. It is argued that such morphologically complex numeral quantifiers (NQs) are semantically complex as well: The numeral within the NQ is the quantifier itself, the classifier its domain of quantification. The proposed analysis offers a unified semantic account of floated and non-floated NQs that adheres closely to their surface morphology and syntax. It (...) explains why floated NQs generally force a distributive reading. It covers both classifiers construed with objects and classifiers construed with events. In addition, it captures the fact that the classifier must agree with the NP it is construed with. (shrink)

This article describes a novel pattern of interpretations associated with universal determiners like ‘each’ and ‘every’. It is demonstrated that these canonically distributive quantifiers can give rise to surprising collective readings when they quantify into sub-clausal constituents, especially other Determiner Phrases. For instance, ‘two cards from each player’ can be understood to pick out a single assorted deck of cards, one whose contents co-vary with the players. Yet this deck as a whole may be said to participate in a range (...) of collective activities (being shuffled together, being traded en masse, not fitting into a standard pack, etc.). Such examples are shown to differ from more familiar _cumulative_ readings of the same quantifiers. A compositional analysis is offered that generalizes Krifka’s ( 2001 ) method of quantification into speech acts in order to accommodate quantification into a larger class of non-truth-denoting semantic objects, including in these cases, entities. (shrink)

Rooth & Partee (1982) and Rooth (1985) have shown that the English-specific rule-by-rule system of PTQ can be factored out into function application plus two transformations for resolving type mismatch (type lifting and variable binding). Building on these insights, this article proposes a universal system for type-driven translation, by adding two more innovations: local type determination for gaps (generalizing Montague 1973) and a set of semantic filters (extending Cooper 1983). This system, dubbed Cross-Linguistic Semantics (XLS), is shown to account for (...) various phenomena — including scope relations in English and Greenlandic Eskimo, internally headed relative clauses in Lakhota, serial verbs in Yoruba and VP ellipsis in English. (shrink)