Random worlds and maximum entropy

Abstract

Given a knowledge base theta containing first-order and statistical facts, a principled method, called the random-worlds method, for computing a degree of belief that some phi holds given theta is considered. If the domain has size N, then one can consider all possible worlds with domain (1, . . ., N) that satisfy theta and compute the fraction of them in which phi is true. The degree of belief is defined as the asymptotic value of this fraction as N grows large. It is shown that when the vocabulary underlying phi and theta uses constants and unary predicates only, one can in many cases use a maximum entropy computation to compute the degree of belief. Making precise exactly when a maximum entropy calculation can be used turns out to be subtle. The subtleties are explored, and sufficient conditions that cover many of the cases that occur in practice are provided.<>