Infinitary logics and 0–1 laws
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
Infinitary logic and inductive definability over finite structures
Information and Computation
Computing with first-order logic
Selected papers of the 23rd annual ACM symposium on Theory of computing
Computing with infinitary logic
ICDT '92 Selected papers of the fourth international conference on Database theory
Information and Computation
Reflective relational machines
Information and Computation
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
A study of homogeneity in relational databases
Annals of Mathematics and Artificial Intelligence
Definability and Descriptive Complexity on Databases of Bounded Tree-Width
ICDT '99 Proceedings of the 7th International Conference on Database Theory
Fixed-Point Logics on Planar Graphs
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Equivalence in finite-variable logics is complete for polynomial time
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Semantic classifications of queries to relational databases
Proceedings of the 2nd international conference on Semantics in databases
On the computation of approximations of database queries
ADC '04 Proceedings of the 15th Australasian database conference - Volume 27
Relational databases and homogeneity in logics with counting
Acta Cybernetica
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We define a new hierarchy in the class of computable queries to relational databases, in terms of the preservation of equality of theories in fragments of first order logic with bounded number of variables with the addition of counting quantifiers (Ck). We prove that the hierarchy is strict, and it turns out that it is orthogonal with the TIME-SPACE hierarchy defined with respect to Turing machine complexity. We introduce a model of computation of queries to characterize the different layers of our hierarchy which is based on the reflective relational machine of S. Abiteboul, C. Papadimitriou, and V. Vianu and where databases are represented by their Ck theories. Then we define and study several properties of databases related to homogeneity in Ck getting various results on the increase of computation power of the introduced machine.