The recent usage control model (UCON) is a foundation for next-generation access control models with distinguishing properties of decision continuity and attribute mutability. A usage control decision is determined by combining authorizations, obligations, and conditions, presented as UCONABC core models by Park and Sandhu. This paper attempts to identify some of the necessary extensions of the usage control model to express a number of discretionary access control policies for relational data management systems. Based on these core aspects, we propose an extension to the authorization core models that concerns negative authorization which permits specification of explicit denial for a user to access an object under a particular mode.