Region Connection Calculus

The region connection calculus (RCC) serves for qualitative spatial representation and reasoning. RCC abstractly describes regions (in Euclidian space, or in a topological space) by their possible relations to each other. RCC8 consists of 8 basic relations that are possible between two regions:
* disconnected (DC)
* externally connected (EC)
* equal (EQ)
* partially overlapping (PO)
* tangential proper part (TPP)
* tangential proper part inverse (TPPi)
* non-tangential proper part (NTPP)
* non-tangential proper part inverse (NTPPi)From these basic relations, combinations can be built. For example, proper part (PP) is the union of TPP and NTPP.

Composition Table

The composition table of RCC8 are as follows:

* "*" denotes the universal relation.

Examples

The RCC8 calculus can be used for reasoning about spatial configurations. Consider the following example: two houses are connected via a road. Each house is located on an own property. The first house possibly touches the boundary of the property; the second one surely does not. What can we infer about the relation of the second property to the road?

The spatial configuration can be formalized in RCC8 as the following constraint network:

house1 DC house2 house1 {TPP, NTPP} property1 house1 {DC EC} property2 house1 EC road house2 { DC, EC } property1 house2 NTPP property2 house2 EC road property1 { DC, EC } property2 road { DC, EC, TPP, TPPi, PO, EQ, NTPP, NTPPi } property1 road { DC, EC, TPP, TPPi, PO, EQ, NTPP, NTPPi } property2

Using the RCC8 composition table and the path-consistency algorithm, we can refine the network in the following way: road { PO, EC } property1 road { PO, TPP } property2

That is, the road either overlaps with the second property, or is even (tangential) part of it.

Other versions of the region connection calculus include RCC5 (with only five basic relations - the distinction whether two regions touch each other are ignored) and RCC23 (which allows reasoning about convexity)..

References

* Randell, D. A., Cui, Z. and Cohn, A. G.: A spatial logic based on regions and connection, Proc. 3rd Int. Conf. on Knowledge Representation and Reasoning, Morgan Kaufmann, San Mateo, pp. 165–176, 1992.
* Anthony G. Cohn, Brandon Bennett, John Gooday, Micholas Mark Gotts: Qualitative Spatial Representation and Reasoning with the Region Connection Calculus. GeoInformatica, 1, 275–316, 1997.
* J. Renz: [http://www.springerlink.com/content/d5g7fcjkd0q2/ Qualitative Spatial Reasoning with Topological Information] . Lecture Notes in Computer Science 2293, Springer Verlag, 2002.