In a seminal work, K. Segerberg introduced deontic action logic (DAL) as a formal framework to investigate normative reasoning over actions. In this work, we revisit DAL and provide a complete algebraization for it. To this end, we introduce deontic action algebras—algebraic structures consisting of a Boolean algebra for interpreting actions, a Boolean algebra for interpreting formulas, and two mappings from one Boolean algebra to the other interpreting the deontic concepts of permission and prohibition. We show how this framework supports the derivation of various deontic action logics by imposing or relaxing structural conditions on either Boolean algebra. This flexibility allows us to uniformly account for several logics within the broader DAL family. In particular, we introduce four variations obtained by: (a) enriching the algebra of formulas with propositions on states, (b) adopting a Heyting algebra for state propositions, (c) adopting a Heyting algebra for actions, and (d) adopting Heyting algebras for both. We illustrate these new deontic action logics with examples and establish their algebraic completeness.
