Decomposing Modal Quantification

Abstract

Providing a compositional interpretation procedure for discourses in which descriptions of complex dependencies between interrelated objects are incrementally built is a key challenge for natural language semantics. This article focuses on the interactions between the entailment particle therefore, modalized conditionals and modal subordination. It shows that the dependencies between individuals and possibilities that emerge out of such interactions can receive a unified compositional account in a system couched in classical type logic that integrates and simplifies van den Berg's dynamic plural logic and the classical Lewis-Kratzer analysis of modal quantification. The main proposal is that modal quantification is a composite notion, to be decomposed in terms of discourse reference to quantificational dependencies that is multiply constrained by the various components that make up a modal quantifier. The system captures the truth-conditional and anaphoric components of modal quantification in an even-handed way and, unlike previous accounts, makes the propositional contents contributed by modal constructions available for subsequent discourse reference.