The study of canonically complete attribute-based access control (ABAC) languages is relatively new. A canonically complete language is useful as it is functionally complete and provides a "normal form" for policies. However, previous work on canonically complete ABAC languages requires that the set of authorization decisions is totally ordered, which does not accurately reflect the intuition behind the use of the allow, deny and not-applicable decisions in access control. A number of recent ABAC languages use a fourth value and the set of authorization decisions is partially ordered. In this paper, we show how canonical completeness in multi-valued logics can be extended to the case where the set of truth values forms a lattice. This enables us to investigate the canonical completeness of logics having a partially ordered set of truth values, such as Belnap logic, and show that ABAC languages based on Belnap logic, such as PBel, are not canonically complete. We then construct a canonically complete four-valued logic using connections between the generators of the symmetric group (defined over the set of decisions) and unary operators in a canonically suitable logic. Finally, we propose a new authorization language @math , an extension of , which incorporates a lattice-ordered decision set and is canonically complete. We then discuss how the advantages of @math can be leveraged within the framework of XACML.
Attribute-based access control (ABAC) has attracted considerable interest in recent years, resulting in an extensive literature on the subject, including the standardized XML-based language XACML. ABAC policies written in languages like XACML have a tree-like structure in which leaf nodes are associated with authorization decisions and non-leaf nodes are associated with decision-combining algorithms. In this paper, we consider the expressive power of the rule- and policy-combining algorithms defined by the XACML standard. In particular, we identify unexpected dependencies between the combining algorithms and demonstrate that there exist useful combining algorithms that cannot be expressed by any combination of XACML combining algorithms. We briefly discuss the decision operators defined in the PTaCL language, an abstract language for defining ABAC policies, and the advantages of replacing the XACML combining algorithms with the PTaCL operators. Following this, we review results in the literature on multi-valued logic and introduce the notion of canonically complete policy languages. We discuss important practical advantages of canonically complete policy languages, primarily in simplifying policy specification and providing efficiently enforceable policies. Finally, we propose a new policy authorization language PTaCL which is canonically complete and show it is capable of expressing any arbitrary policy in a normal form and discuss the advantages of using PTaCL over existing policy languages such as XACML and PTaCL.