Obligations and permissions, algebraically

We further develop the algebraic approach to input/output logic initiated in \cite{wollic22}, where subordination algebras and a family of their generalizations were proposed as a semantic environment of various input/output logics. In particular, we consider precontact algebras as a suitable algebraic environment for negative permission, and we characterize properties of several types of permission (negative, static, dynamic), as well as their interactions with normative systems, by means of suitable modal languages encoding outputs.