This paper describes a novel method for allowing an autonomous ground vehicle to predict the intent of other agents in an urban environment. This method, termed the cognitive driving framework, models both the intent and the potentially false beliefs of an obstacle vehicle. By modeling the relationships between these variables as a dynamic Bayesian network, filtering can be performed to calculate the intent of the obstacle vehicle as well as its belief about the environment. This joint knowledge can be exploited to plan safer and more efficient trajectories when navigating in an urban environment. Simulation results are presented that demonstrate the ability of the proposed method to calculate the intent of obstacle vehicles as an autonomous vehicle navigates a road intersection such that preventative maneuvers can be taken to avoid imminent collisions.