Anaphoric Linking at Run Time: A Type-Logical Account of Discourse Representation
Kazushige Terui

Abstract:
Anaphoric Linking at Run Time: 
  A Type-Logical Account of Discourse Representation
Kazushige Terui

A number of attempts have been made to combine Discourse Representation 
Theory with type-logical grammar in order to obtain a compositional 
(bottom-up) framework for discourse representation (e.g., Muskens, van 
Eijck & Kamp). In those attempts, how- ever, it is usually assumed that 
anaphoric links are given in advance of the construction of discourse 
representation structures (DRSs). This assumption causes a difficulty, 
typically dealing with plural anaphora, because generally suitable 
referents of plural pronouns are not present before the construction, 
but should be created through the construction of DRSs.

To settle this difficulty, we shall propose a new type-logical framework 
of DRT in which anaphoric linking takes place during the construction of 
DRSs (Run Time Anaphoric Linking). The construction is bottom-up in the 
sense that it is based on the sequent calculus proof search of Lambek 
calculus. We exploit quantifier types to represent the run time anaphoric 
linking mechanism. We shall briefly illustrate how plural anaphora are 
treated in our framework. In particular, we shall show that Summation and 
Abstraction, which are used to create suitable antecedent discourse 
referents for plural pronouns in [KR93], are available in our type-logical 
setting using the linear logic modality.