Integrating cardinal direction relations and other orientation relations in Qualitative Spatial Reasoning

Integrating different knowledge representation languages is one of the main topics in Qualitative Spatial Reasoning (QSR). Existing languages are generally incomparable in terms of expressive power; as such, their integration compensates each other’s representational deficiencies, and is seen by real applications, such as Geographic Information Systems (GIS), or robot navigation, as an answer to the well-known poverty conjecture of qualitative languages in general, and of QSR languages in particular. Knowledge expressed in such an integrating language decomposes then into parts, or components, each expressed in one of the integrated languages. Reasoning internally within each component of such knowledge involves only the language the component is expressed in, which is not new. The challenging question is to come with methods for the interaction of the different components of such knowledge. With these considerations in mind, we propose a calculus, cCOA, integrating two calculi well-known in QSR: Frank’s projection-based cardinal direction calculus, CDA, and a coarser version, ROA, of Freksa’s relative orientation calculus. An original constraint propagation procedure, PcS4c+(), for cCOACSPs is presented, which aims at (1) achieving path consistency (Pc) for the CDA projection; (2) achieving strong 4-consistency (S4c) for the ROA projection; and (3) more (+) —the “+” consists of the implementation of the interaction between the two integrated calculi. Dealing with the first two points is not new, and involves mainly the CDA composition table and the ROA composition table, which can be found in, or derived from, the literature. The originality of the propagation algorithm comes from the last point. Two tables, one for each of the two directions CDA-to-ROA and ROA-to-CDA, capturing the interaction between the two kinds of knowledge, are defined, and used by the algorithm. The importance of taking into account the interaction is shown with a real example providing an inconsistent knowledge base, whose inconsistency (a) cannot be detected by reasoning separately about each of the two components of the knowledge, just because, taken separately, each is consistent, but (b) is detected by the proposed algorithm, thanks to the interaction knowledge propagated from each of the two compnents to the other.