We look at the relatively unexplored problem of plan recognition applied to motion in 2-D environments where all moving objects are modelled as circles. Golog is a well-known high level logical language for solving planning problems and specifying agent controllers. Few studies have applied Golog to plan recognition. We use some of the features of this language, but its standard interpreter is adapted to solving plan recognition problems.This thesis makes several other contributions. First, plan recognition procedures are formulated as finite automata and expressed as Golog programs. Second, we elaborate a logical formalism for reasoning about depth and motion from an observer's viewpoint. We not only expand on this situation calculus based formalism, but also apply it to tackle plan recognition problems in the traffic domain. The proposed approach is implemented and thoroughly tested on recognizing simple behaviours such as left turns, right turns, and overtaking.