Incremental interpretation and dynamic semantics

The goal of this paper is to motivate and define a strictly incremental semantics for dynamic predicate logic (Groenendijk and Stokhof 1991). In particular, we will extend the incremental semantics for dynamic propositional logic introduced in Vermeulen (1994) to first-order predicate logic (borrowing central notions from Visser 2002). We call the resulting logical system Incremental Dynamic Predicate Logic and we show how this system can be used to derive correct truth conditions for apparently non-incremental structures like donkey conditionals in a strictly incremental fashion. That is, the correct meanings for donkey conditionals are derived by means of a strictly left-to-right compositional procedure. This is accomplished without having to type-shift the meanings of the individual words (as in Steedman 2001, for example), and with dynamic conjunction / sequencing as the only compositional operation.