Asymptotic Conditional Probabilities: The Unary Case

@article{Grove1996AsymptoticCP,
  title={Asymptotic Conditional Probabilities: The Unary Case},
  author={Adam J. Grove and Joseph Y. Halpern and Daphne Koller},
  journal={SIAM J. Comput.},
  year={1996},
  volume={25},
  pages={1-51}
}
Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for first-order sentences. Given first-order sentences $\phi$ and $\theta$, we consider the structures with domain $\{1,\ldots, N\}$ that satisfy $\theta$, and compute the fraction of them in which $\phi$ is true. We then consider what happens to this fraction as $N$ gets large. This extends the work on 0-1 laws that considers the limiting probability of… 

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