Trivalent Semantics for Conditional Obligations

This paper provides a new framework for formalizing conditional obligations in nat- ural language: it pairs a unary deontic operator with trivalent semantics for the indicative conditional and the assumption that the antecedents of conditionals re- strict 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 addresses classical challenges such as the “if A then ought A” problem, the paradox of the miners, and the modeling of contrary-to-duty obligations (viz. Chisholm’s quartet). All in all, our proposal provides a unified account of deontic modals and conditionals thatsquares well with general theories of natural language reasoning.