Random Worlds and Maximum Entropy (1994)
| Venue: | In Proc. 7th IEEE Symp. on Logic in Computer Science |
| Citations: | 44 - 12 self |
BibTeX
@ARTICLE{Grove94randomworlds,
author = {Adam J. Grove and Joseph Y. Halpern and Daphne Koller},
title = {Random Worlds and Maximum Entropy},
journal = {In Proc. 7th IEEE Symp. on Logic in Computer Science},
year = {1994},
volume = {2},
pages = {22--33}
}
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Abstract
Given a knowledge base KB containing first-order and statistical facts, we consider a principled method, called the random-worlds method, for computing a degree of belief that some formula ' holds given KB . If we are reasoning about a world or system consisting of N individuals, then we can consider all possible worlds, or first-order models, with domain f1; : : : ; Ng that satisfy KB , and compute the fraction of them in which ' is true. We define the degree of belief to be the asymptotic value of this fraction as N grows large. We show that when the vocabulary underlying ' and KB uses constants and unary predicates only, we can naturally associate an entropy with each world. As N grows larger, there are many more worlds with higher entropy. Therefore, we can use a maximum-entropy computation to compute the degree of belief. This result is in a similar spirit to previous work in physics and artificial intelligence, but is far more general. Of equal interest to the result itself are...
