This work tackles the risk estimation problem from a new perspective: a framework is proposed for reasoning about traffic situations and collision risk at a semantic level, while classic approaches typically reason at a trajectory level. Risk is assessed by estimating the intentions of drivers and detecting conflicts between them, rather than by predicting the future trajectories of the vehicles and detecting collisions between them. More specifically, dangerous situations are identified by comparing what drivers intend to do with what they are expected to do according to the traffic rules. The reasoning about intentions and expectations is performed in a probabilistic manner, in order to take into account sensor uncertainties and interpretation ambiguities. This framework can in theory be applied to any type of traffic situation; here we present its application to the specific case of road intersections. The proposed motion model takes into account the mutual influences between the maneuvers performed by vehicles at an intersection. It also incorporates information about the influence of the geometry and topology of the intersection on the behavior of a vehicle, and therefore can be applied to arbitrary intersection layouts. The approach was validated with field trials using passenger vehicles equipped with Vehicle-to-Vehicle wireless communication modems, and in simulation. The results demonstrate that the algorithm is able to detect dangerous situations early and complies with real-time constraints.