Formal Semantics in Modern Type Theories

4Advanced Modification

Adjectival and adverbial modification has been troubling formal semanticists since the early days of Montague Grammar (see, for example, (Montague 1970, 1974; Kamp 1975; Parsons 1972) among others). It was clear from these early days that modification was not an easy problem to tackle. Indeed, providing adequate semantic accounts of modification has proven a difficult task. One of the reasons for this is that the adjectival/adverbial classes are largely non-homogeneous semantic classes where a strict classification according to semantic properties is quite challenging. This semantic non-homogeneity renders the task of providing formal semantic accounts that will be able to generalize across adjectival and adverbial classes very difficult.

In section 3.3, adjectival modification has been studied for MTT-semantics according to a traditional classification. In this chapter, we look at more fine-grained aspects of adjectival and adverbial modification. Our goal is to show that the rich structures and expressiveness of MTTs can form the basis for an adequate account of modification in natural language.¹ Some notes on unaccounted and problematic aspects will be given at the end of the chapter, suggesting routes for future research.

4.1. The data

Let us start with a basic similarity and a basic distinction between adverbs and adjectives: both are modifiers of some sort. However, adjectives are noun modifiers, while adverbs are verbal or sentential modifiers. ...