On the representation and estimation of spatial uncertainly
International Journal of Robotics Research
Effective solution of qualitative interval constraint problems
Artificial Intelligence
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)
Relation algebras of intervals
Artificial Intelligence
Qualitative representation of positional information
Artificial Intelligence
A new approach to cyclic ordering of 2D orientations using ternary relation algebras
Artificial Intelligence
A relation — algebraic approach to the region connection calculus
Theoretical Computer Science
Qualitative Representation of Spatial Knowledge
Qualitative Representation of Spatial Knowledge
Robot Motion Planning
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
Qualitative Spatial Representation and Reasoning Techniques
KI '97 Proceedings of the 21st 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
Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
Cognitively adequate modelling of spatial reference in human-robot interaction
ICTAI '00 Proceedings of the 12th IEEE International Conference on Tools with Artificial Intelligence
Composing cardinal direction relations
Artificial Intelligence
Modeling and Computing Ternary Projective Relations between Regions
IEEE Transactions on Knowledge and Data Engineering
Wayfinding choremes-a language for modeling conceptual route knowledge
Journal of Visual Languages and Computing
Spatial knowledge representation for human-robot interaction
Spatial cognition III
Projective relations for 3D space: computational model, application, and psychological evaluation
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
SC'04 Proceedings of the 4th international conference on Spatial Cognition: reasoning, Action, Interaction
Pointing to space: modeling of deictic interaction referring to regions
Proceedings of the 5th ACM/IEEE international conference on Human-robot interaction
Qualitative reasoning with directional relations
Artificial Intelligence
A model of spatial reference frames in language
COSIT'11 Proceedings of the 10th international conference on Spatial information theory
Qualitative reasoning about relative direction of oriented points
Artificial Intelligence
Orientation calculi and route graphs: towards semantic representations for route descriptions
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
StarVars: effective reasoning about relative directions
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Qualitative spatial reasoning (QSR) abstracts metrical details of the physical world. The two main directions in QSR are topological reasoning about regions and reasoning about orientations of point configurations. Orientations can refer to a global reference system, e.g. cardinal directions or instead only to relative orientation, e.g. egocentric views. Reasoning about relative orientations poses additional difficulties compared to reasoning about orientations in an absolute reference frame. Qualitative knowledge about relative orientation can be naturally expressed in the form of ternary point calculi. Designing such calculi requires compromising between desired mathematical properties and the power to describe and model concrete ''real-world'' problems. Research has shown that using basic notions such as granularity leads to imprecise reasoning and as a consequence to underdetermined knowledge which is difficult to handle efficiently. Concrete problems need a combination of qualitative knowledge of orientation and qualitative knowledge of distance. We present a calculus based on ternary relations where we introduce a qualitative distance measurement based on two of the three points. Its main advantage is that it utilizes finer distinctions than previously published calculi. Furthermore, it permits differentiations which are useful in realistic application scenarios such as robot navigation that cannot be directly dealt with in coarser calculi.