The complexity of elementary algebra and geometry
Journal of Computer and System Sciences
Languages that capture complexity classes
SIAM Journal on Computing
Handbook of theoretical computer science (vol. B)
Selected papers of the 9th annual ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Topological queries in spatial databases
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Relational expressive power of constraint query languages
Journal of the ACM (JACM)
Querying spatial databases via topological invariants
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
First-Order Queries on Finite Structures Over the Reals
SIAM Journal on Computing
Relational queries over interpreted structures
Journal of the ACM (JACM)
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Constraint Databases
On Topological Elementary Equivalence of Spatial Databases
ICDT '97 Proceedings of the 6th International Conference on Database Theory
Linear vs Polynomial Constraints in Database Query Languages
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
On Expressing Topological Connectivity in Spatial Datalog
CDB '97 Second International Workshop on Constraint Database Systems, Constraint Databases and Their Applications
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
On first-order topological queries
ACM Transactions on Computational Logic (TOCL)
Deciding Termination of Query Evaluation in Transitive-Closure Logics for Constraint Databases
ICDT '03 Proceedings of the 9th International Conference on Database Theory
DBPL '01 Revised Papers from the 8th International Workshop on Database Programming Languages
On First-Order Topological Queries
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Theoretical Computer Science - Database theory
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It is known that standard query languages for constraint databases lack the power to express connectivity properties. Such properties are important in the context of geographical databases, where one naturally wishes to ask queries about connectivity (what are the connected components of a given set?) or reachability (is there a path from A to B that lies entirely in a given region?). No existing constraint query languages that allow closed form evaluation can express these properties.In the first part of the paper, we show that in principle there is no obstacle to getting closed languages that can express connectivity and reachability queries. In fact, we show that adding any topological property to standard languages like FO + LIN and FO+POLY results in a closed language. In the second part of the paper, we look for tractable closed languages for expressing reachability and connectivity queries. We introduce path logic, which allows one to state properties of paths with respect to given regions. We show that it is closed, has polynomial time data complexity for linear and polynomial constraints, and can express a large number of reachability properties beyond simple connectivity. Query evaluation in the logic involves obtaining a discrete abstraction of a continuous path, and model-checking of temporal formulae on the discrete structure.