Introduction

Can the notion of [±sqa] be captured in terms of generalized quantification? This question was raised in Verkuyl (1987a) concerning what can be called Standard GQT. This subsumes all work on generalized quantification based on the assumption that NPs are of type <<e,t>,t>, that is, that they denote collections of sets. The answer given was roughly: a determiner Det of an NP yields a [±sq]-NP if and only if the intersection of the two sets standing in the Detrelation is bounded, that is, finite and non-empty. This answer is not satisfactory: (a) it does not cover the question of whether or not the [+sqa]-property is related to any of the well known constraints on quantifiers, such as monotonicity, strength, properness, and so on; (b) there are apparent counterexamples which have not yet been dealt with; and (c) the conditions under which an NP may express [-sqa]-information were not sufficiently described.

The characterization of [+sqa] at the <<e,t>,t>-level will be summarized in section 4.1. It will be made clear that there is an interesting difference between the so-called mathematical meanings of at least n and at most n on the one hand and their meaning in sentences expressing temporal structure. In section 4.2, attention will be paid to some of the major constraints on Generalized Quantifiers having emerged in the eighties, in order to see in section 4.3 whether or not [+sqa] may be associated with one of them.