Versatility of 'Continuations' in Discourse Semantics

We show in this paper how the computer science concept of ’continuations’, together with categorial grammars and a type shifting mechanism, is able to account for a wide range of natural language semantic phenomena, such as hierarchical discourse structure, ellipses, accommodation and free-focus and bound-focus anaphora. The merit of continuations in the dynamic semantics framework is that they abstract away from assignment functions that are essential to the formulations of Dynamic Intensional Logic, Dynamic Montague Grammar, Dynamic Predicate Logic and Discourse Representation Theory, Thus, continuation style semantic do not pose problems such as the destructive assignment problem in Dynamic Predicate Logic or the variable clash problem in Discourse Representation Theory. We argue that continuations are a versatile and powerful tool, particularly well suited to manipulate scope and long distance dependencies, phenomena that abound in natural language semantics.