 The modal information theory approach to multi-agent information flow is the subject of a great amount of research. The semantics is not always carried out in relational terms (i.e., with Kripke Frames) but is done often algebraically (see Blackburn et al. 2001 for details of the algebraic approach to modal logic). For more details on algebraic as well as type-theoretic approaches, see the subsection on algebraic and other approaches to modal information theory in the supplementary document  Abstract Approaches to Information Structure.