How Conditionals Restrict

Abstract

Conditionals restrict modal domains: in sentences of the form A > MODAL B, the modal quantifies only over worlds where the antecedent is true. This paper has two aims. The first is to derive these data axiomatically for basic modals, giving a logic for the conditional which has as theorems the axiomatic regimentations of the restrictor data. The second is to show that this logic does not require the conditional to be a pure restrictor, as in Kratzer (1981) and Kratzer (1991); it is sound on a restricting operator semantics, where conditionals shift worlds and accessibility relations. The restricting operator semantics offers a picture whereby conditionals can restrict without that being their only semantic function, thus sidestepping a notorious difficulty for Kratzer’s semantics, the existence of bare conditionals.