Relational queries computable in polynomial time
Information and Control
Datalog extensions for database queries and updates
Journal of Computer and System Sciences
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
A restricted second order logic for finite structures
Information and Computation
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Annals of Mathematics and Artificial Intelligence
The Relational Polynomial-Time Hierarchy and Second-Order Logic
Semantics in Data and Knowledge Bases
Elements of Finite Model Theory
Elements of Finite Model Theory
A Second-Order Logic in Which Variables Range over Relations with Complete First-Order Types
SCCC '10 Proceedings of the 2010 XXIX International Conference of the Chilean Computer Science Society
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We introduce a restriction of second order logic, SOF, for finite structures. In this restriction the quantifiers range over relations closed by the equivalence relation ≡FO. In this equivalence relation the equivalence classes are formed by k-tuples whose First Order type is the same, for some integer k≥1. This logic is a proper extension of the logic SOω defined by A. Dawar and further studied by F. Ferrarotti and the second author. In the existential fragment of SOF, $\Sigma^{1,F}_1$ , we can express rigidity, which cannot be expressed in SOω. We define the complexity class NPF by using a variation of the relational machine of S. Abiteboul and V. Vianu (RMF) and we prove that this complexity class is captured by $\Sigma^{1,F}_1$ . Then we define an RMFk machine with a relational oracle and show the exact correspondence between prenex fragments of SOF and the levels of the PHF polynomial-time hierarchy.