n previous work, we have studied the
<I>random-worlds</I> 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 based on well-known
approaches, such as <I>cross-entropy</I>.  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.<p>