realistic way. The identity of a crossing revisited after a cyclic path is not given but has to be inferred which makes navigation much more challenging. Since there are many ambiguities left, the task is to track the multiple geometrically possible topologies of the network during an incremental observation. Thus, the goal of Wallgrun's qualita- ¨ tive mapping algorithm is to process the history of observations and determine all route graph hypotheses which can be considered valid explanations so far. This consistency checking can be based on qualitative spatial reasoning about positions. The local relative observation are modeled based on *OPRA*2 expressions about o-points in a similar way like in the street network described above.

![0_image_0.png](0_image_0.png)

A comprehensive simulation which uses the *OPRA*4 calculus for an important subtask was built by Dylla et. al. [2]. Their system called SailAway simulates the behavior of different vessels following declarative (written) navigation rules for collision avoidance. This system can be used to verify whether a given set of rules leads to stable avoidance between potentially colliding vessels The different vessel categories that determine their right of way priorities are represented in an ontology. The movement of the vessels is described by a method called conceptual neighborhood-based reasoning (CNH reasoning). CNH reasoning describes whether two spatial configurations of objects can be transformed into each other by small changes [6], [9]. A CNH transformation can be a object movement in a short period of time. Fig. 10 shows a CNH
transition diagram which represents relative trajectories of two rule following vessels.

The depicted sequence between two vessels A and B is:
A 4∠
0 0 B → A 4∠
1 1 B → A 4∠
2 2 B → A 4∠
3 3 B . Based on this qualitative representation of trajectories, CNH reasoning is used as a simple, abstract model of the navigation of the potentially colliding vessels in the SailAway simulator [2])2.

These three applications above make use of qualitative spatial reasoning with OPRA2 or *OPRA*4 in simulated spatial agent scenarios. The granularity m = 2 can model straight continuation and right angles which are important for representing idealized street networks. The granularities m = 2 and m = 4 also correspond to earlier work about computational models of linguistic projective expressions (left, right, in front, behind) by Moratz et. al. [16] [18]. The applications presented in this section could benefit from additional qualitative relative distance knowledge. The TPCC calculus presented by Moratz & Ragni [17] is a first step towards this direction. However,