Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
Communications of the ACM
Relation algebras over containers and surfaces: An ontological study of a room space
Spatial Cognition and Computation
INDU: An Interval and Duration Network
AI '99 Proceedings of the 12th Australian Joint Conference on Artificial Intelligence: Advanced Topics in Artificial Intelligence
Simple Models for Simple Calculi
COSIT '99 Proceedings of the International Conference on Spatial Information Theory: Cognitive and Computational Foundations of Geographic Information Science
When Tables Tell It All: Qualitative Spatial and Temporal Reasoning Based on Linear Orderings
COSIT 2001 Proceedings of the International Conference on Spatial Information Theory: Foundations of Geographic Information Science
Towards a Complete Classification of Tractability in Point Algebras for Nonlinear Time
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
The complexity of constraint satisfaction problems for small relation algebras
Artificial Intelligence
Spatial and temporal reasoning: beyond Allen's calculus
AI Communications - Special issue on: Spatial and temporal reasoning
A spatial odyssey of the interval algebra: 1. directed intervals
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Weak representations of interval algebras
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
On generalized interval calculi
AAAI'91 Proceedings of the ninth National conference on Artificial intelligence - Volume 1
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This paper argues for considering qualitative spatial and temporal reasoning in algebraic and category-theoretic terms. A central notion in this context is that of weak representation (WR) of the algebra governing the calculus. WRs are ubiquitous in qualitative reasoning, appearing both as domains of interpretation and as constraints. Defining the category of WRs allows us to express the basic notion of satisfiability (or consistency) in a simple way, and brings clarity to the study of various variants of consistency. The WRs of many popular calculi are of interest in themselves. Moreover, the classification of WRs leads to non-trivial model-theoretic results. The paper provides a not-too-technical introduction to these topics and illustrates it with simple examples.