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). 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 (cCOA Constraint Satisfaction Problems) is presented, which aims at (1) achieving path consistency for the CDA projection; (2) achieving strong 4-consistency for the ROA projection; and (3) more (+) --the "+" consists of the implementation of the interaction between the two combined calculi. 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.

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