Coarse deontic logic

Cariani (Ought and resolution semantics) has proposed a semantics for ought that combines two features: (i) it invalidates Inheritance, i.e. the inference from ought to ought whenever is logically weaker than , and it does so in a principled manner; (ii) it allows for coarseness, which means that ought can be true even if there are specific ways of making true that are (intuitively speaking) impermissible.we present a family of multi-modal logics based on Cariani's proposal and a more recent criticism by Bronfmann and Dowell (2018, Oxford Handbook of Reasons). We study the formal properties of these logics in detail and show how they can be translated into normal multi-modal logics. Using well-known techniques, we establish a sound and (strongly) complete axiomatisation for each of these and show them to satisfy the finite model property. In addition, we compare them to existing approaches in the deontic logic literaturemost notably Anglberger et al.'s logic of obligation as weakest permission and Horty's deontic STIT logic.