Combining cardinal direction relations and relative orientation relations in Qualitative Spatial Reasoning

Combining 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 combination compensates each other’s representational deficiencies, and is seen as an answer to the emerging demand from real applications, such as Geographical Information Systems (GIS), robot navigation, or shape description, for the representation of more specific knowledge than is allowed by each of the languages taken separately. Knowledge expressed in such a combined language decomposes then into parts, or components, each expressed in one of the combined 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, combining, thus more expressive than each of, two calculi well-known in QSR: Frank’s cardinal direction calculus, CDA, and a coarser version, ROA, of Freksa’s relative orientation calculus. An original constraint propagation procedure, PcS4c+(), for cCOA-CSPs 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 combined 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.