A Dynamic Categorial Grammar

We present a compositional, dynamic categorial grammar for discourse analysis that captures the core insights of dynamic semantics: indefinites do not quantify but introduce discourse referents; definites are anaphoric to previously-mentioned discourse referents; discourse referents have their ‘lifespan’ limited by certain operators. The categorial grammar formalism we propose is strongly lexicalist and derives linguistic signs with a syntactic division of labor separating surface form from the underlying combinatorics. We argue that this formalism compares favorably with earlier efforts on several counts. It does not require any complicated or idiosyncratic machinery such as specialized assignments, states, or continuations, and encodes the requirement that a certain discourse referent be present in the discourse context using dependent types, rather than e.g. partial functions. The dynamic semantics itself is a straightforward extension of an underlying static semantics that is fully (hyper)intensional, avoiding many unsavory problems associated with standard possible worlds approaches.