Abstract

This paper provides a new framework for formalizing conditional obligations in natural language: it pairs a unary deontic operator with trivalent semantics for the indicative conditional and Kratzer's idea that the antecedents of conditionals restrict the scope of modals in the consequent. Combining these three ideas, we obtain a fully compositional theory of "if" and "ought'" that validates plausible principles for deontic reasoning. Moreover, it resolves classical challenges such as the "if A then ought A" problem, the paradox of the miners and the modeling of contrary-to-duty obligations (e.g., Chisholm's quartet). All in all, our proposal is attractive from a logical point of view and squares well with general theories of natural language reasoning.