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0–1 Laws for Fragments of Existential Second-Order Logic: A Survey

  • Phokion G. Kolaitis
  • Moshe Y. Vardi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1893)

Abstract

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 Σ1 1 fragments are identical, but the classifications are different without equality.

Keywords

Decision Problem Random Graph Relation Symbol Extension Axiom Countable Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Phokion G. Kolaitis
    • 1
  • Moshe Y. Vardi
    • 2
  1. 1.University of CaliforniaSanta CruzUSA
  2. 2.Rice UniversityUSA

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