Journal of the ACM (JACM)
Hierarchical reasoning about direction relations
GIS '96 Proceedings of the 4th ACM international workshop on Advances in geographic information systems
A new approach to cyclic ordering of 2D orientations using ternary relation algebras
Artificial Intelligence
Double-Crossing: Decidability and Computational Complexity of a Qualitative Calculus for Navigation
COSIT 2001 Proceedings of the International Conference on Spatial Information Theory: Foundations of Geographic Information Science
Reasoning about Binary Topological Relations
SSD '91 Proceedings of the Second International Symposium on Advances in Spatial Databases
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
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
On generalizing orientation information in OPRAm
KI'06 Proceedings of the 29th annual German conference on Artificial intelligence
Inferring and distributing spatial context
EuroSSC'07 Proceedings of the 2nd European conference on Smart sensing and context
Qualitative spatial representation and reasoning in the SparQ-toolbox
SC'06 Proceedings of the 2006 international conference on Spatial Cognition V: reasoning, action, interaction
A qualitative approach to localization and navigation based on visibility information
COSIT'09 Proceedings of the 9th international conference on Spatial information theory
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
CLP(QS): a declarative spatial reasoning framework
COSIT'11 Proceedings of the 10th international conference on Spatial information theory
Qualitative reasoning about relative direction of oriented points
Artificial Intelligence
Projective relations in a 3d environment
GIScience'06 Proceedings of the 4th international conference on Geographic Information Science
A condensed semantics for qualitative spatial reasoning about oriented straight line segments
Artificial Intelligence
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In this paper, a ternary qualitative calculus ${\mathcal LR}$ for spatial reasoning is presented that distinguishes between left and right. A theory is outlined for ternary point-based calculi in which all the relations are invariant when all points are mapped by rotations, scalings, or translations (RST relations). For this purpose, we develop methods to determine arbitrary transformations and compositions of RST relations. We pose two criteria which we call practical and natural. ‘Practical' means that the relation system should be closed under transformations, compositions and intersections and have a finite base that is jointly exhaustive and pairwise disjoint. This implies that the well-known path consistency algorithm [10] can be used to conclude implicit knowledge. ‘Natural' calculi are close to our natural way of thinking because the base relations and their complements are connected. The main result of the paper is the identification of a maximally refined calculus amongst the practical natural RST calculi, which turns out to be very similar to Ligozat's flip-flop calculus. From that it follows, e.g., that there is no finite refinement of the TPCC calculus by Moratz et al that is closed under transformations, composition, and intersection.