Topological queries in spatial databases
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Querying spatial databases via topological invariants
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Maintaining knowledge about temporal intervals
Communications of the ACM
A Tractable Subclass of the Block Algebra: Constraint Propagation and Preconvex Relations
EPIA '99 Proceedings of the 9th Portuguese Conference on Artificial Intelligence: Progress 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
Disjunctive Temporal Reasoning in Partially Ordered Models of Time
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
A new tractable subclass of the rectangle algebra
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Composing cardinal direction relations
Artificial Intelligence
A Family of Directional Relation Models for Extended Objects
IEEE Transactions on Knowledge and Data Engineering
Categorical methods in qualitative reasoning: the case for weak representations
COSIT'05 Proceedings of the 2005 international conference on Spatial Information Theory
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In [8] Bennett, Isli and Cohn put out the following challenge to researchers working with theories based on composition tables (CT): give a general characterization of theories and relational constraint languages for which a complete proof procedure can be specified by a CT. For theories based on CTs, they make the distinction between a weak, consistency-based interpretation of the CT, and a stronger extensional definition. In this paper, we take up a limited aspect of the challenge, namely, we characterize a subclass of formalisms for which the weak interpretation can be related in a canonical way to a structure based on a total ordering, while the strong interpretations have the property of aleph-zero categoricity (all countable models are isomorphic). Our approach is based on algebraic, rather than logical, methods. It can be summarized by two keywords: relation algebra and weak representation.