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Asymptotic Conditional Probabilities: The Non-unary Case

by Adam J. Grove, Joseph Y. Halpern, Daphne Koller - J. SYMBOLIC LOGIC , 1993
"... 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 ' and `, we consider the structures with domain f1; : : : ; Ng that satisfy `, and compute the fra ..."
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the fraction of them in which ' 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 considering asymptotic conditional probabilities. As shown by Liogon'kii [Lio69
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