reference direction.

Since intrinsic and extrinsic references are closely related in the rest of the paper, we sometimes refer to QSR calculi which use either intrinsic or extrinsic reference systems as relative position QSR calculi. Then, the two terms *local reference systems* and *relative reference systems* refer to the same concept.

An interesting special case refers to the representation of a relative orientation without the concept of distance. These relative orientations can be viewed as decoupled from anchor points. Then there is no means for distinguishing between different point locations. The great advantage is that much more efficient reasoning mechanisms become available. The work by Isli and Cohn [19] consists of a ternary calculus for reasoning about such pure orientations. In contrast to relative position calculi, their algebra has a tractable subset containing the base relations.

Absolute (or global) directions can relate directional knowledge from distant places to each other. Cardinal directions as an example can be registered with a compass and compared over a large distance. And for that reason Frank's cardinal direction calculus corresponds to such an absolute reference system [9],
[20]. There is a variant of a cardinal direction calculus, which has a flexible granularity, the Star Calculus [21].

In the previous paragraphs, we discussed the *representation* of spatial knowledge. Another important aspect are the *reasoning* mechanisms which are employed to make use of the represented initial knowledge to infer indirect knowledge. In Qualitative Spatial Reasoning two main reasoning modes are used: Conceptual neighbourhood-based reasoning, and constraint-based reasoning about (static) spatial configurations. Conceptual neighborhood-based reasoning describes whether two spatial configurations of objects can be transformed into each other by small changes [22]. The conceptual neighborhood of a qualitative spatial relation which holds for a spatial arrangement is the set of relations into which a relation can be changed with minimal transformations, e.g. by continuous deformation. Such a transformation can be a movement of one object in the configuration in a short period of time. At the discrete level of concepts, the neighborhood corresponds to continuity on the geometric or physical level of description: continuous processes map onto identical or neighboring classes of descriptions [23]. Spatial conceptual neighborhoods are very natural perceptual and cognitive entities and other neighborhood structures can be derived from spatial neighborhoods, e.g. temporal neighborhoods.

The movement of an agent can then be modeled qualitatively as a sequence of neighboring spatial relations which hold for adjacent time intervals3. Based on this qualitative representation of trajectories, neighborhood-based spatial reasoning can for example be used as a simple, abstract model of the navigation of a spatial agent4.

In constraint-based reasoning about spatial configurations, typically a partial initial knowledge of a scene is represented in terms of qualitative constraints be-3This was the reasoning used in the first investigation of dipole relations by Schlieder [24]
4for an application of neighbourhood based reasoning of spatial agents, we refer the reader to the simulation model SAILAWAY [25]