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 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.