Constraint propagation algorithms for temporal reasoning: a revised report
Readings in qualitative reasoning about physical systems
Journal of Symbolic Computation
Complexity and algorithms for reasoning about time: a graph-theoretic approach
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
A new approach to cyclic ordering of 2D orientations using ternary relation algebras
Artificial Intelligence
Maintaining knowledge about temporal intervals
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Reasoning about Binary Topological Relations
SSD '91 Proceedings of the Second International Symposium on Advances in Spatial Databases
Computational Properties of Qualitative Spatial Reasoning: First Results
KI '95 Proceedings of the 19th Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Using Orientation Information for Qualitative Spatial Reasoning
Proceedings of the International Conference GIS - From Space to Territory: Theories and Methods of Spatio-Temporal Reasoning on Theories and Methods of Spatio-Temporal Reasoning in Geographic Space
A Symbolic Approach to Interval Constraint Problems
AISMC-1 Proceedings of the International Conference on Artificial Intelligence and Symbolic Mathematical Computation
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Modeling and Computing Ternary Projective Relations between Regions
IEEE Transactions on Knowledge and Data Engineering
Qualitative spatial reasoning about relative point position
Journal of Visual Languages and Computing
Qualitative Reasoning about Convex Relations
Proceedings of the international conference on Spatial Cognition VI: Learning, Reasoning, and Talking about Space
Reachability and dependency calculi: reasoning in network algebras
SC'06 Proceedings of the 2006 international conference on Spatial Cognition V: reasoning, action, interaction
Qualitative spatial representation and reasoning in the SparQ-toolbox
SC'06 Proceedings of the 2006 international conference on Spatial Cognition V: reasoning, action, interaction
Qualitative reasoning with directional relations
Artificial Intelligence
A much better polynomial time approximation of consistency in the LR calculus
Proceedings of the 2010 conference on STAIRS 2010: Proceedings of the Fifth Starting AI Researchers' Symposium
SC'04 Proceedings of the 4th international conference on Spatial Cognition: reasoning, Action, Interaction
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The Double Cross calculus has been proposed for the purpose of navigation based on qualitative information about spatial configurations. Up until now, however, no results about algorithmic properties of this calculus are known. First, we explore the possibility of applying constraint propagation techniques to solve the reasoning problem in this calculus. For this purpose, we have to generalize the known techniques for binary relations because the Double Cross calculus is based on ternary relations. We will show, however, that such a generalization leads to problems. The Double Cross calculus is not closed under composition and permutation. Further, as we will show, there exists no finite refinement of the base relations with such a closure property. Finally, we show that determining satisfiability of constraint systems over Double Cross relations is NP-hard, even if only the base relations of the Double Cross calculus are used. On the positive side, however, we show that the reasoning problem is solvable in PSPACE.