A definition of secure dependencies using the logic of security

In the context of the modal logic of security, confidentiality is defined by the formula K_Bφ→R_B φ that could be read `If B knows φ then B should have the permission to know φ´. The authors propose a new semantics for the R_B modal operator, such that the definition of security would allow a certain number of dependencies (called secure dependencies) between objects of the system. They formally compare this definition of security with non-interference, non-deducibility and generalized non-interference, especially with respect to assumptions on the systems as non-determinism and input-totalness