This paper proposes a D-algebra to compose decisions from multiple access control policies. Compared to other algebrabased approaches aimed at policy composition, D-algebra is the only one that satisfies both functional completeness (any possible decision matrix can be expressed by a D-algebra formula) and computational effectiveness (a formula can be computed efficiently given any decision matrix). The Dalgebra has several relevant applications in the context of access control policies, namely the analysis of policy languages decision mechanisms, and the development of tools for policy authoring and enforcement. Categories and Subject Descriptors C.2.0 [Computer Communication Networks]: General-security and protection; D.4.6 [Operating Systems]: Security and Protection--Access Controls; K.6.5 [Management of Computing and Information Systems]: Security and Protection General Terms Management, Security, Standardization Keywords Many-valued Logic, MV-Algebras, Policy Composition, Decisi...