An intelligent agent will often be uncertain about various properties
of its environment, and when acting in that environment it will freque
ntly need to quantify its uncertainty. For example, if the agent wishe
s to employ the expected-utility paradigm of decision theory to guide
its actions, it will need to assign degrees of belief (subjective prob
abilities) to various assertions. Of course, these degrees of belief s
hould not be arbitrary, but rather should be based on the information
available to the agent. This paper describes one approach for inducing
degrees of belief from very rich knowledge bases, that can include in
formation about particular individuals, statistical correlations, phys
ical laws, and default rules. We call our approach the random-worlds m
ethod. The method is based on the principle of indifference: it treats
all of the worlds the agent considers possible as being equally likel
y. It is able to integrate qualitative default reasoning with quantita
tive probabilistic reasoning by providing a language in which both typ
es of information can be easily expressed. Our results show that a num
ber of desiderata that arise in direct inference (reasoning from stati
stical information to conclusions about individuals) and default reaso
ning follow directly from the semantics of random worlds. For example,
random worlds captures important patterns of reasoning such as specif
icity, inheritance, indifference to irrelevant information, and defaul
t assumptions of independence. Furthermore, the expressive power of th
e language used and the intuitive semantics of random worlds allow the
method to deal with problems that are beyond the scope of many other
nondeductive reasoning systems.