We often reach conclusions partially on the basis that we do not have evidence that the conclusion is false. A newspaper story warning that the local water supply has been contaminated would prevent a person from drinking water from the tap in her home. This suggests that the absence of such evidence contributes to her usual belief that her water is safe. On the other hand, if a reasonable person received a letter telling her that she had won a million dollars, she would consciously consider whether there was any evidence that the letter was a hoax or somehow misleading before making plans to spend the money. All to often we arrive at conclusions which we later retract when contrary evidence becomes available. The contrary evidence defeats our earlier reasoning. Much of our reasoning is defeasible in this way. Since around 1980, considerable research in AI has focused on how to model reasoning of this sort. In this paper, I describe one theoretical approach to this problem, discuss implementation of this approach as an extension of Prolog, and describe some application of this work to normative reasoning, learning, planning, and other types of automated reasoning.

We describe a new approach to default reasoning, based on a principle of indifference among possible worlds. We interpret default rules as extreme statistical statements, thus obtaining a knowledge base KB comprised of statistical and first-order statements. We then assign equal probability to all worlds consistent with KB in order to assign a degree of belief to a statement '. The degree of belief can be used to decide whether to defeasibly conclude '. Various natural patterns of reasoning, such as a preference for more specific defaults, indifference to irrelevant information, and the ability to combine independent pieces of evidence, turn out to follow naturally from this technique. Furthermore, our approach is not restricted to default reasoning; it supports a spectrum of reasoning, from quantitative to qualitative. It is also related to other systems for default reasoning. In particular, we show that the work of [ Goldszmidt et al., 1990 ] , which applies maximum entropy ideas t...

How should what one knows about an individual affect default conclusions about that individual? This paper contrasts two views of "knowledge" in default reasoning systems. The first is the traditional view that one knows the logical consequences of one's knowledge base. It is shown how, under this interpretation, having to know an exception is too strong for default reasoning. It is argued that we need to distinguish "background" and "contingent" knowledge in order to be able to handle specificity, and that this is a natural distinction. The second view of knowledge is what is contingently known about the world under consideration. Using this view of knowledge, a notion of conditioning that seems like a minimal property of a default is defined. Finally, a qualitative version of the lottery paradox is given; if we want to be able to say that individuals that are typical in every respect do not exist, we should not expect to conclude the conjunction of our default conclusions. This paper...

This paper presents a logical formalism for representing and reasoning with statistical knowledge. One of the key features of the formalism is its ability to deal with qualitative statistical information. It is argued that statistical knowledge, especially that of a qualitative nature, is an important component of our world knowledge and that such knowledge is used in many different reasoning tasks. The work is further motivated by the observation that previous formalisms for representing probabilistic information are inadequate for representing statistical knowledge. The representation mechanism takes the form of a logic that is capable of representing a wide variety of statistical knowledge, and that possesses an intuitive formal semantics based on the simple notions of sets of objects and probabilities defined over those sets. Furthermore, a proof theory is developed and is shown to be sound and complete. The formalism offers a perspicuous and powerful representational tool for stat...