Coordinate representation of order types requires exponential storage
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Modelling topological and metrical properties in physical processes
Proceedings of the first international conference on Principles of knowledge representation and reasoning
Journal of the ACM (JACM)
Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
Qualitative representation of positional information
Artificial Intelligence
Curves and surfaces in geometric modeling: theory and algorithms
Curves and surfaces in geometric modeling: theory and algorithms
A new approach to cyclic ordering of 2D orientations using ternary relation algebras
Artificial Intelligence
Maintaining knowledge about temporal intervals
Communications of the ACM
Efficient Processing of Spatial Queries in Line Segment Databases
SSD '91 Proceedings of the Second International Symposium on Advances in Spatial Databases
Similarity of Cardinal Directions
SSTD '01 Proceedings of the 7th International Symposium on Advances in Spatial and Temporal Databases
Qualitative Spatial Representation and Reasoning Techniques
KI '97 Proceedings of the 21st Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Representation and Processing of Qualitative Orientation Knowledge
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
Region connection calculus: its models and composition table
Artificial Intelligence
Composing cardinal direction relations
Artificial Intelligence
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
Representing Relative Direction as a Binary Relation of Oriented Points
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
The design and experimental analysis of algorithms for temporal reasoning
Journal of Artificial Intelligence Research
Qualitative and quantitative representations of locomotion and their application in robot navigation
IJCAI'99 Proceedings of the 16th international joint conference on Artificial intelligence - Volume 2
Qualitative CSP, finite CSP, and SAT: comparing methods for qualitative constraint-based reasoning
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Customizing qualitative spatial and temporal calculi
AI'07 Proceedings of the 20th Australian joint conference on Advances in artificial intelligence
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 spatial reasoning with topological information
Qualitative spatial reasoning with topological information
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Qualitative reasoning with directional relations
Artificial Intelligence
SC'04 Proceedings of the 4th international conference on Spatial Cognition: reasoning, Action, Interaction
Exploiting qualitative spatial neighborhoods in the situation calculus
SC'04 Proceedings of the 4th international conference on Spatial Cognition: reasoning, Action, Interaction
Qualitative reasoning about relative direction of oriented points
Artificial Intelligence
Hi-index | 0.00 |
More than 15 years ago, a set of qualitative spatial relations between oriented straight line segments (dipoles) was suggested by Schlieder. However, it turned out to be difficult to establish a sound constraint calculus based on these relations. In this paper, we present the results of a new investigation into dipole constraint calculi which uses algebraic methods to derive sound results on the composition of relations of dipole calculi. This new method, which we call condensed semantics, is based on an abstract symbolic model of a specific fragment of our domain. It is based on the fact that qualitative dipole relations are invariant under orientation preserving affine transformations. The dipole calculi allow for a straightforward representation of prototypical reasoning tasks for spatial agents. As an example, we show how to generate survey knowledge from local observations in a street network. The example illustrates the fast constraint-based reasoning capabilities of dipole calculi. We integrate our results into two reasoning tools which are publicly available.