Journal of the ACM (JACM)
Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
Communications of the ACM
Fast algebraic methods for interval constraint problems
Annals of Mathematics and Artificial Intelligence
Point algebras for temporal reasoning: algorithms and complexity
Artificial Intelligence
Spatial and temporal reasoning: beyond Allen's calculus
AI Communications - Special issue on: Spatial and temporal reasoning
Spatial and temporal reasoning: beyond Allen's calculus
AI Communications - Spatial and Temporal Reasoning
The 9 + -Intersection: A Universal Framework for Modeling Topological Relations
GIScience '08 Proceedings of the 5th international conference on Geographic Information Science
Customizing qualitative spatial and temporal calculi
AI'07 Proceedings of the 20th Australian joint conference on Advances in artificial intelligence
Inferring additional knowledge from QTCN relations
Information Sciences: an International Journal
Dependency calculus: reasoning in a general point relation algebra
KI'05 Proceedings of the 28th annual German conference on Advances in Artificial Intelligence
Categorical methods in qualitative reasoning: the case for weak representations
COSIT'05 Proceedings of the 2005 international conference on Spatial Information Theory
The head-body-tail intersection for spatial relations between directed line segments
GIScience'06 Proceedings of the 4th international conference on Geographic Information Science
Topological relations of arrow symbols in complex diagrams
Diagrams'06 Proceedings of the 4th international conference on Diagrammatic Representation and Inference
Exploiting qualitative spatial neighborhoods in the situation calculus
SC'04 Proceedings of the 4th international conference on Spatial Cognition: reasoning, Action, Interaction
Journal of Ambient Intelligence and Smart Environments
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Allen's well-known Interval Algebra has been developed for temporal representation and reasoning, but there are also interesting spatial applications where intervals can be used. A prototypical example are traffic scenarios where cars and their regions of influence can be represented as intervals on a road as the underlying line. There are several differences of temporal and spatial intervals which have to be considered when developing a spatial interval algebra. In this paper we analyze the first important difference: as opposed to temporal intervals, spatial intervals can have an intrinsic direction with respect to the underlying line. We develop an algebra for qualitative spatial representation and reasoning about directed intervals, identify tractable subsets, and show that path-consistency is sufficient for deciding consistency for a particular subset which contains all base relations.