From statistical knowledge bases to degrees of belief: an overview

• Authors: Joseph Y. Halpern
• Venue: Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
• Year: 2006

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, she 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 provides a brief overview of 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. The approach is called 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. 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. The relevance of the random-worlds method to database systems is also discussed.