# 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…

## 32 Citations

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