Semantics circle: Bounded variables

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Abstract

On one mainstream view, presupposition projection exploits a notion of local context. On a recent theory developed by Matt Mandelkern, the domains of epistemic modals are constrained by information states, which  Mandelkern calls "bounds". Local contexts and bounds project in very similar ways, and seem to be part of the same broad system. But they are not quite the same thing: as Mandelkern points out, there are clear extensional differences between the two in some environments. I propose a system that links the two, effectively unifying Mandelkern's theory of modals and a Schlenker-style theory of presupposition projection. The key idea is that every clause includes a context variable---a variable that picks out a set of worlds. Like local contexts, context variables track the information that is available at a certain stage in the compositional computation. But context variables are interpreted locally and can be bound. The resulting theory solves empirical and conceptual difficulties for Mandelkern's system, while using a simpler architecture.