  We establish a novel connection between two research areas in non-classical
logics which have been developed independently of each other so far: on the one
hand, input/output logic, introduced within a research program developing
logical formalizations of normative reasoning in philosophical logic and AI; on
the other hand, subordination algebras, investigated in the context of a
research program integrating topological, algebraic, and duality-theoretic
techniques in the study of the semantics of modal logic. Specifically, we
propose that the basic framework of input/output logic, as well as its
extensions, can be given formal semantics on (slight generalizations of)
subordination algebras. The existence of this interpretation brings benefits to
both research areas: on the one hand, this connection allows for a novel
conceptual understanding of subordination algebras as mathematical models of
the properties and behaviour of norms; on the other hand, thanks to the well
developed connection between subordination algebras and modal logic, the output
operators in input/output logic can be given a new formal representation as
modal operators, whose properties can be explicitly axiomatised in a suitable
language, and be systematically studied by means of mathematically established
and powerful tools.
