Type-theoretical semantics with coercive subtyping

Abstract

In the formal semantics based on modern type theories, common nouns are interpreted as types, rather than as functional subsets of entities as in Montague grammar. This brings about important advantages in linguistic interpretations but also leads to a limitation of expressive power because there are fewer operations on types as compared with those on functional subsets. The theory of coercive subtyping adequately extends the modern type theories with a notion of subtyping and, as shown in this paper, plays a very useful role in making type theories more expressive for formal semantics. In particular, it gives a satisfactory treatment of the type-theoretic interpretation of modified common nouns and allows straightforward interpretations of interesting linguistic phenomena such as copredication, whose interpretations have been found difficult in a Montagovian setting. We shall also study some type-theoretic constructs that provide useful representational tools for formal lexical semantics, including how the so-called dot-types for representing logical polysemy may be expressed in a type theory with coercive subtyping.