Daphne Koller's thesis From Knowledge to Belief
When acting in the real world, an intelligent agent must make decisions under uncertainty. For example, a doctor may need to decide upon the treatment for a particular patient. The standard solution to this problem is based on decision theory. It requires the agent to assign degrees of belief or sub jective probabilities to the relevant assertions. The degrees of belief assigned should be based on the information available to the agent. A doctor, for example, may have information about particular patients, statistical correlations between symptoms and diseases, physical laws, default rules, and more. This thesis describes one approach, called the random-worlds method, for inducing degrees of belief from very rich knowledge bases.
The random-worlds method is based on the principle of indi�erence: it treats as equally likely all the worlds that the agent considers possible. It deals with knowledge bases expressed in a language that augments rst-order logic with statistical statements. By interpreting default rules as qualitative statistics, the approach integrates qualitative default reasoning with quantitative probabilistic reasoning. The thesis shows that a large number of desiderata that arise in direct inference (reasoning from statistical information to conclusions about individuals) and in default reasoning follow provably from the semantics of random worlds. Thus, random worlds naturally derives important patterns of reasoning such as speci city, inheritance, indi�erence to irrelevant information, and a default assumption of independence. Furthermore, the expressive power of random worlds and its intuitive semantics allow it to deal well with examples that are too complex for most other inductive reasoning systems.
The thesis also analyzes the problem of computing degrees of belief according to random worlds. This analysis uses techniques from nite model theory and zero-one laws. We show that, in general, the problem of computing degrees of belief is undecidable, even for knowledge bases with no statistical information. On the other hand, for knowledge bases that involve only unary predicates, there is a tight connection between the random-worlds method and the principle of maximum entropy. In fact, maximum entropy can be used as a computational tool for computing degrees of belief in many practical cases.
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