On Decision-Theoretic Foundations for Defaults

Abstract

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. We accept a default if it ignores states with small impact according to our measure. We motivate our choice of measures and show that the r es ulting formalization of defaults satisfies desired properties of defaults, namely 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.