Challenge Problems for a Theory of Degree Multiplication (with partial answer key)

Abstract

This paper offers a theory of degree multiplication in natural language semantics. Motivation for the development such a theory comes from proportional readings of quantity words and rate expressions such as miles per hour. After laying out a set of ‘challenge problems’ that any good theory of degree multiplication should be able to handle, I set about solving them, borrowing mathematical tools from quantity calculus. These algebraic foundations are integrated into a compositional Montagovian framework, yielding a system that can solve, or partially solve, some of the problems.