The problem of interpreting the trajectories of a person (user) moving in a spatial environment is fundamental for the design of any location-based application. We argue that in order to correctly assign a meaning to the spatial behavior encoded by the trajectory, it is necessary to express the meaning in terms of the user's intentions, more specifically, the goals that the user intends to achieve. Along the trajectory, these intentions will change frequently because the user's initial goal is decomposed into sequences of subgoals. The paper proposes a representational formalism and a reasoning mechanism for knowledge about an agent who acts according to changing intentions: spatially grounded intentional systems. An objective consists in making the representation as expressive as possible without running into a behavior interpretation problem that is computationally intractable. The approach is shown to be sufficiently expressive to model the interaction between intentions and behavior in a location-based game, CityPoker.