Default Inferences From Statistical Knowledge

There are two common and distinct uses of probabilities: probabilities used as degrees of belief and probabilities used as statistical measures. Probabilities used as statistical measures can represent various assertions about the objective statistical state of the world, while probabilities used as degrees of belief 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 certain probabilistic degrees of beliefs in other assertions based on these statistics. For example, an agent who knows that most birds fly (a statistical fact) may have 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 know as direct inference. We develop a formal logical mechanism for performing direct inference, and demonstrate how this mechanism can be applied to the problem of making default inferences as studied in AI.