Deontic Action Logics via Algebra.

Deontic logics are dubbed the logics of normative or prescriptive reasoning. These logics can roughly be categorized into ought-to-be, dealing with the prescription of state of a airs, or ought-to-do, dealing with the prescription of actions. An important family of ought-to-do deontic logics have their origin in Segerberg's Deontic Action Logic (DAL, see [23]). In this work, we provide an algebraic characterization of DAL and some known variants. In brief, we capture actions and formulas as elements of different base algebras, and deontic operators as algebraic operations; di erent algebras capture the di erent variants. This algebraization enables us to obtain completeness results via standard algebraic means. Moreover, we argue that this algebraic framework o ers a natural way of (re-)thinking many deontic logical issues at large.