Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Conceptual Spaces: The Geometry of Thought
Conceptual Spaces: The Geometry of Thought
Using Hierarchical Spatial Data Structures for Hierarchical Spatial Reasoning
COSIT '97 Proceedings of the International Conference on Spatial Information Theory: A Theoretical Basis for GIS
Geocognostics - A New Framework for Spatial Information Theory
COSIT '97 Proceedings of the International Conference on Spatial Information Theory: A Theoretical Basis for GIS
A New Framework for Reasoning about Points, Intervals and Durations
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on 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
The Map-Learning Critter
A Virtual Test Bed in Support of Cognitively-Aware Geomatics Technologies
COSIT 2001 Proceedings of the International Conference on Spatial Information Theory: Foundations of Geographic Information Science
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In this paper, we explore the situation where no cardinal directions or globally available orientations are available and no metric estimates are given. This corresponds to the way many people perceive their environment and carry out spatial reasoning tasks. We consider three kinds of locally available information – proximity (nearest neighbor), relevance (different sets of neighbors) and distribution (alignments) – and we limit our interest to a universe of point objects. We show how the theory of manifolds and sheaves can be applied to the problem of combining locally available information of a qualitative nature into a global model of an environmental space. We then explore the limitations of the resulting global model if information capture is incomplete or uncertain. Finally, we note that some indeterminacy in the global model does not entail difficulties for a user, provided the reasoning task is appropriately constrained or appropriate additional information is used, such as an external reference.