Proceedings of the Annual Meeting of the Cognitive Science Society

The Representation of ignorance is a long standing challenge for researchers in probability and decision theory. During the past decade, Artificial Intelligence researchers have developed a class of reasoning systems, called Truth Maintenance Systems, which are able to reason on the basis of incomplete information. In this paper we will describe a new method for dealing with partially specified probabilistic models, by extending a logic-based truth maintenance method from Boolean truth-values to probability intervals. Then we will illustrate how this method can be used to represent Bayesi&n Belief Networks — one of the best known formalisms to reason under uncertainty — thus producing a new class of Bayesian Belief Networks, caUed Ignorant Belief Networks, able to reason on the basis of partially specified prior and conditional probabilities. Finally, we will discuss how this new method relates to some theoretical intuitions and empirical findings in decision theory and cognitive science.