Alethic-Deontic Logic and the Alethic-Deontic Octagon

This paper will introduce and explore a set of alethic-deontic systems. Alethic-deontic logic is a form of logic that combines ordinary (alethic) modal logic, which deals with modal concepts such as necessity, possibility and impossibility, and deontic logic, which investigates normative expressions such as “ought”, “right” and “wrong”. I describe all the systems axiomatically. I say something about their properties and prove some theorems in and about them. We will be especially interested in how the different deontic and modal concepts are related to each other in various systems. We will map these relationships in an alethic-deontic octagon, a figure similar to the classical so-called square of opposition.