Untyped sets, invention, and computable queries
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Generic Computation and its complexity
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Infinitary logics and 0–1 laws
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
Feasible computation through model theory
Feasible computation through model theory
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
Fixpoint logics, relational machines, and computational complexity
Journal of the ACM (JACM)
Reflective relational machines
Information and Computation
A restricted second order logic for finite structures
Information and Computation
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Annals of Mathematics and Artificial Intelligence
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
SOF: a semantic restriction over second-order logic and its polynomial-time hierarchy
Conceptual Modelling and Its Theoretical Foundations
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We explore the connection between the concept of relational complexity introduced by S. Abiteboul, M. Vardi and V. Vianu and the restricted second-order logic SO 茂戮驴 introduced by A. Dawar. In relational complexity, the basis for measuring the complexity of computing queries with relational machines, is the number of different FO k-types realized by the input database. In SO 茂戮驴, the second-order quantifiers range over relations that are closed under equality of FO k-types of k-tuples. We give a direct proof (in the style of the proof of Fagin's theorem) of the result of A. Dawar on the fact that the existential fragment of SO 茂戮驴 captures relationalNP. Then we define formally the concept of relational machine with relational oracleand show the exact correspondence between the prenex fragments of SO 茂戮驴 and the levels of the relationalpolynomial-time hierarchy.