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