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 * A preliminary version of this 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 nondeductive reasoning systems. E Bacchus et cd. /Arrificiul Intelligence 87 (I 996) 75-143 t? Bucchus et ul. /Artijiciul Intelligence 87 (I 996) 75-143 4 These "individuals" might be complex objects (such as sequences of coin tosses) depending on what we take as primitive in our ontology. s Although the examples in this section deal with reasoning about single individuals, in general both referenceclass reasoning and random worlds can be applied to queries such as "Did Eric infect Tom", which involve reasoning about a number of individuals simultaneously. In such cases the reference classes will consist of sets of ruples of individuals. E Bacchus et al. /Artificial Intelligence 87 (1996) 75-143 81 E Bacclu~~ et d./Art$cial lnielligence 87 (1996) 75-143 l Right Weakening. If qo + I++ is logically valid and KB k p, then KB i_ @. l Reflexivity. KB k KB. l Left Logical Equivalence. If KB H KB' is logically valid, then KB /--p if and only if KB' b 40. l Cut. If KB k 6, and KB A 0 f--cp then KB i_ p. l Cautious Monotonic&.