Deontic logic

Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. Typically, a deontic logic uses OA to mean it is obligatory that A, (or it ought to be (the case) that A), and PA to mean it is permitted (or permissible) that A. The term deontic is derived from the ancient Greek déon - δέον (gen.: δέοντος), meaning, roughly, that which is binding or proper.

In von Wright's first system, obligatoriness and permissibility were treated as features of acts. It was found not much later that a deontic logic of propositions could be given a simple and elegant Kripke-style semantics, and von Wright himself joined this movement. The deontic logic so specified came to be known as "standard deontic logic," often referred to as SDL, KD, or simply D. It can be axiomatized by adding the following axioms to a standard axiomatization of classical propositional logic:

In English, these axioms say, respectively:

FA, meaning it is forbidden that A, can be defined (equivalently) as ${\displaystyle O\lnot A}$ or ${\displaystyle \lnot PA}$.

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