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A security policy of an information system is a set of security requirements that correspond to permissions, prohibitions and obligations to execute some actions when some contextual conditions are satisfied. Traditional approaches consider that the information system enforces its associated security policy if and only if actions executed in this system are permitted by the policy (if the policy is closed) or not prohibited (if the policy is open) and every obligatory actions are actually executed in the system (no violation of obligations). In this paper, we investigate a more sophisticated approach in which an information system specification is compliant with its security policy even though some security requirements may be violated. Our proposal is to consider that this is acceptable when the security policy specifies additional requirements that apply in case of violation of other security requirements. In this case, we formally define conditions to be satisfied by an information system to comply with its security policy. We then present a proof-based approach to check if these conditions are enforced.

We study logical properties that concern the preservation of future-directed obligations that have not been fulfilled yet. Our starting point is a product of temporal and deontic logics. We investigate some modifications of the semantics of the product in order to satisfy preservation properties, without loosing too much of the basic properties of the product. We arrive at a semantics in which we only consider ideal histories that share the same past as the current one, and that enables a characterization of the states in which the obligations propagate. These are the states where any obligation of a formula that concerns the present moment is not violated. When there are such violations, the deontic realm switches to a lower level of ideality.