The decision problem for the probabilities of higher-order properties
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Discrete Mathematics
0-1 laws and decision problems for fragments of second-order logic
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
Asymptotic probabilities of existential second-order Go¨del sentences
Journal of Symbolic Logic
Information and Computation
Finitistic proofs of 0-1 laws for fragments of second-order logic
Information Processing Letters
Theoretical Computer Science
Journal of the ACM (JACM)
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Fragments of Existential Second-Order Logic without 0-1 Laws
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Untestable properties in the kahr-moore-wang class
WoLLIC'11 Proceedings of the 18th international conference on Logic, language, information and computation
Testable and untestable classes of first-order formulae
Journal of Computer and System Sciences
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The probability of a property on the collection of all finite relational structures is the limit as n → ∞ of the fraction of structures with n elements satisfying the property, provided the limit exists. It is known that the 0-1 law holds for every property expressible in first-order logic, i.e., the probability of every such property exists and is either 0 or 1. Moreover, the associated decision problem for the probabilities is solvable. In this survey, we consider fragments of existential second-order logic in which we restrict the patterns of first-order quantifiers. We focus on fragments in which the first-order part belongs to a prefix class. We show that the classifications of prefix classes of first-order logic with equality according to the solvability of the finite satisfiability problem and according to the 0-1 law for the corresponding +11 fragments are identical, but the classifications are different without equality.