Alethic-Deontic Logic : Deontic Accessibility Defined in Terms of Alethic Accessibility

According to many normative theories, to say that something ought to be, or ought to be done, is to state that the being or doing of this thing is in some sense a necessary condition (requirement) of something else. In this paper, I explore the consequences of such a view. I consider what kind of alethic-deontic logic is appropriate for theories of this sort. Alethic-deontic logic is a kind of bimodal logic that combines ordinary alethic (modal) logic and deontic logic. Ordinary alethic logic is a branch of logic that deals with modal concepts, such as necessity and possibility, modal sentences, arguments and systems. Deontic logic is the logic of norms. It deals with normative words, such as ought, right and wrong, normative sentences, arguments and systems. I will define the so-called deontic accessibility relation in terms of the so-called alethic accessibility relation, and I will examine the consequences of this definition. It will turn out that a particular alethic-deontic system, Strong alethic-deontic logic, is plausible given this definition. By adding a certain frame-condition, the accessibility condition, we obtain a slightly stronger system, Full alethic-deontic logic. Some of the technical details of these systems are briefly described. Most of the systems mentioned in this paper are developed in more detail elsewhere.