Obligations and permissions on selfextensional logics

Abstract We further develop the abstract algebraic logic approach to input/output logic initiated in (De Domenico, International Workshop on Logic, Language, Information, and Computation 326–343, 2022), where the family of selfextensional logics was proposed as a general background environment for input/output logics. In this paper, we introduce and discuss the generalizations of several types of permission (negative, dual negative, static, dynamic), as well as their interactions with normative systems, to various families of selfextensional logics, thereby proposing a systematic approach to the definition of normative and permission systems on nonclassical propositional bases.