Brasoveanu, Adrian 2007. Structured Discourse Reference to Individuals, to appear in the Proceedings of the 6th Discourse Anaphora and Anaphor Resolution Colloquium. 

The paper argues that discourse reference in natural language involves two equally important components with essentially the same interpretive dynamics, namely reference to values, i.e. (non-singleton) sets of individuals, and reference to structure, i.e. the correlation / dependency between such sets, which is introduced and incrementally elaborated upon in discourse. To define and investigate structured discourse reference, a new dynamic system couched in classical (many-sorted) type logic is introduced which extends Compositional DRT (Muskens 1996) with plural information states, i.e. information states are modeled as sets of variable assignments (following van den Berg 1996), which can be can be represented as matrices with assignments (sequences) as rows. A plural info state encodes both values (the columns of the matrix store sets of objects) and structure (each row of the matrix encodes a correlation / dependency between the objects stored in it). Given the underlying type logic, compositionality at sub-clausal level follows automatically and standard techniques from Montague semantics (e.g. type shifting) become available. The idea that plural info states are semantically necessary is motivated by relative-clause donkey sentences with multiple singular anaphors: (i) mixed reading (weak & strong) sentences: Every person who buys a book on amazon.com and has a credit card uses it to pay for it; (ii) sentences exemplifying donkey anaphora to structure: Every boy who bought a Christmas gift for a girl in his class asked her deskmate to wrap it.