Background Notions in Lattice Theory and Generalized Quantifiers

Abstract

Many papers in this volume build on certain elementary notions of lattice theory and generalized quantifier theory; often, their empirical predictions derive directly from them. The goal of this chapter is to enable readers who have some background in formal semantics, but not in these particular areas, to appreciate the pertinent papers. But readers who are familiar with lattices and GQs may also find the discussion useful because, elementary as it is, it highlights certain aspects that other literature may not. On the other hand, precisely because this chapter is geared towards particular applications, it does not attempt to cover issues that a standard introduction would, when they do not seem directly relevant here.

This chapter is based on my lecture notes for classes given at UCLA, the University of Budapest, and the 1993 LS A Linguistic Institute. I thank the participants of these courses for feedback. Work on the present version was partially supported by NSF grant #9222501.