Asymptotic Conditional Probabilities: The Non-Unary Case

@article{Grove1996AsymptoticCP,
title={Asymptotic Conditional Probabilities: The Non-Unary Case},
author={Adam J. Grove and Joseph Y. Halpern and Daphne Koller},
journal={J. Symb. Log.},
year={1996},
volume={61},
pages={250-276}
}

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 φ and θ, we consider the structures with domain {1, . . . , N} that satisfy θ, and compute the fraction of them in which φ 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 first-order sentences, by… CONTINUE READING