From Statistical Knowledge Bases to Degrees of Belief
  An intelligent agent will often be uncertain about various properties of its
environment, and when acting in that environment it will frequently need to
quantify its uncertainty. For example, if the agent wishes to employ the
expected-utility paradigm of decision theory to guide its actions, it will need
to assign degrees of belief (subjective probabilities) to various assertions.
Of course, these degrees of belief should 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 information about particular individuals, statistical correlations,
physical laws, and default rules. We call our approach the random-worlds
method. The method is based on the principle of indifference: it treats all of
the worlds the agent considers possible as being equally likely. It is able to
integrate qualitative default reasoning with quantitative probabilistic
reasoning by providing a language in which both types of information can be
easily expressed. Our results show that a number of desiderata that arise in
direct inference (reasoning from statistical information to conclusions about
individuals) and default reasoning follow directly {from} the semantics of
random worlds. For example, random worlds captures important patterns of
reasoning such as specificity, inheritance, indifference to irrelevant
information, and default assumptions of independence. Furthermore, the
expressive power of the language used and the intuitive semantics of random
worlds allow the method to deal with problems that are beyond the scope of many
other non-deductive reasoning systems.
