Standard Polyadic Lifts

Abstract

This chapter is devoted to a logical and computational study of multi-quantifier sentences, like: ‘Three explorers discovered most of the islands.’ First, I show how to compositionally construct the meaning of such sentences from the meaning of single quantifiers using special semantic operations known as polyadic lifts, i.e., iteration, cumulation, and resumption. Next, I discuss how to extend semantic automata model to cover some of the polyadic quantifiers and the cognitive reality of such extension. As in the case of monadic quantifiers, this leads to a question about the limits of polyadic quantification in natural language. I discuss a popular answer, known as Frege’s Thesis: all polyadic quantification in natural language is iterated monadic quantification. I recall classic characterization results of the Frege boundary and ask about its place in Chomsky’s hierarchy. While doing this I emphasize the role of computational/cognitive representations in the formal semantics of natural language.