Default Reasoning From Statistics

Fahiem Bacchus

There are two common but quite distinct interpretations of probabilities: they can be interpreted as a measure of the extent to which an agent believes an assertion, i.e., as an agent’s degree of belief, or they can be interpreted as an assertion of relative frequency, i.e., as a statistical measure. Used as statistical measures probabilities can represent various assertions about the objective statistical state of the world, while used as degrees of belief they can represent various assertions about the subjective state of an agent’s beliefs. In this paper we examine how an agent who knows certain statistical facts about the world might infer probabilistic degrees of beliefs in other assertions from these statistics. For example, an agent who knows that most birds fly (a statistical fact) may generate a degree of belief greater than 0.5 in the assertion that Tweety flies given that Tweety is a bird. This inference of degrees of belief from statistical facts is known as direct inference. We develop a formal logical mechanism for performing direct inference. Some of the inferences possible via direct inference are closely related to default inferences. We examine some features of this relationship.

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