Despite considerable advancements in the area of access control and authorization languages, current approaches to enforcing access control are all based on monolithic and complete specifications. This assumption is too restrictive when access control restrictions to be enforced come from the combination of different policy specifications, each possibly under the control of independent authorities, and where the specifics of some component policies may not even be known a priori. Turning individual specifications into a coherent policy to be fed into the access control system requires a nontrivial combination and translation process. This article addresses the problem of combining authorization specifications that may be independently stated, possibly in different languages and according to different policies. We propose an algebra of security policies together with its formal semantics and illustrate how to formulate complex policies in the algebra and reason about them. A translation of policy expressions into equivalent logic programs is illustrated, which provides the basis for the implementation of the algebra. The algebra's expressiveness is analyzed through a comparison with first-order logic.
As fragments of first-order logic, Description logics (DLs) do not provide nonmonotonic features such as defeasible inheritance and default rules. Since many applications would benefit from the availability of such features, several families of nonmonotonic DLs have been developed that are mostly based on default logic and autoepistemic logic. In this paper, we consider circumscription as an interesting alternative approach to nonmonotonic DLs that, in particular, supports defeasible inheritance in a natural way. We study DLs extended with circumscription under different language restrictions and under different constraints on the sets of minimized, fixed, and varying predicates, and pinpoint the exact computational complexity of reasoning for DLs ranging from ALC to ALCIO and ALCQO. When the minimized and fixed predicates include only concept names but no role names, then reasoning is complete for NExp NP . It becomes complete for NP NExp when the number of minimized and fixed predicates is bounded by a constant. If roles can be minimized or fixed, then complexity ranges from NExp NP to undecidability.
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