The open wording of the traffic rules of the sea, COLREGS, and the existence of unwritten rules, make it essential for an autonomous ship to understand the intentions of meeting traffic. This article uses a dynamic Bayesian network (DBN) to model and infer the intentions of other ships based on their observed real-time behavior. Multiple intention nodes are included to describe the different ways a ship can interpret and conflict with the behavioral rules outlined in CORLEGS. The prior distributions of the intention nodes are adapted to the current situation based on observable characteristics such as location and relative ship size. When a new observation is made, the probability distributions of the intention variables are updated by excluding all combinations of intention states that conflict with the observed behavior. This way of modeling makes the intention probabilities independent of how often observations are made. The resulting model is able to identify situations that are prone to cause misunderstandings and infer the state of multiple intention variables that describe the behavior. Different collision avoidance algorithms can use the resulting intention information to better know if, when, and how to act.