Generating New Beliefs From Old
  In previous work [BGHK92, BGHK93], we have studied the random-worlds approach
-- a particular (and quite powerful) method for generating degrees of belief
(i.e., subjective probabilities) from a knowledge base consisting of objective
(first-order, statistical, and default) information. But allowing a knowledge
base to contain only objective information is sometimes limiting. We
occasionally wish to include information about degrees of belief in the
knowledge base as well, because there are contexts in which old beliefs
represent important information that should influence new beliefs. In this
paper, we describe three quite general techniques for extending a method that
generates degrees of belief from objective information to one that can make use
of degrees of belief as well. All of our techniques are bloused on well-known
approaches, such as cross-entropy. We discuss general connections between the
techniques and in particular show that, although conceptually and technically
quite different, all of the techniques give the same answer when applied to the
random-worlds method.
