Quantification and Reference in Incremental Processing

This paper shows how polymorphic type theory can be used for a compositional incrementalnatural language semantics that can handle singular and plural reference and quantifica-tion, in a setting where context gets dynamically extended. We focus on the treatmentof quantifiers and anaphoric reference in dynamic semantics, and for ease of exposition welimit ourselves to distributive readings of plurals. The approach is illustrated with a frag-ment implemented in the functional programming language Haskell. The paper contains thecomplete Haskell code of our implementation, in ‘literate programming style’.