Curry Typing, Polymorphism, and Fine‐Grained Intensionality
Shalom Lappin · 2015
Montague's framework remains a seminal achievement in formal semantic theory. However, several of its foundational assumptions encounter serious problems when this framework is extended beyond the small fragment of English that Montague formalized. This chapter examines these problems, and considers alternatives to Montague's type theory and his characterization of intensions in order to deal with these problems. It presents a brief summary of the architecture of intensional logic (IL), and discusses some of the difficulties that it raises. The chapter describes Property Theory with Curry Typing (PTCT), a first-order semantic representation system that uses Curry typing with weak polymorphism. It also explains how PTCT provides a formal solution to the problem of fine-grained intensionality through its typed treatment of identity versus equivalence. The chapter presents some programmatic ideas on how one could move beyond classical categorical semantic theories to a probabilistic system that accommodates the pervasive gradience of semantic properties.