On decision-theoretic foundations for defaults

In recent years, considerable effort has gone into understanding default reasoning. Most of this effort concentrated on the question of entailment, i.e., what conclusions are warranted by a knowledge-base of defaults. Surprisingly, few works formally examine the general role of defaults. We argue that an examination of this role is necessary in order to understand defaults, and suggest a concrete role for defaults: Defaults simplify our decision-making process, allowing us to make fast, approximately optimal decisions by ignoring certain possible states. In order to formalize this approach, we examine decision making in the framework of decision theory. We use probability and utility to measure the impact of possible states on the decision-making process. More precisely, we examine when a consequence relation, which is the set of default inferences made by an inference system, can be compatible with such a decision-theoretic setup. We characterize general properties that such consequence relations must satisfy and contrast them with previous analysis of default consequence relations in the literature. In particular, we show that such consequence relations must satisfy the properties of cumulative reasoning. Finally, we compare our approach with Poole's decision-theoretic defaults, and show how both can be combined to form an attractive framework for reasoning about decisions.