Revising Knowledge: A Hierarchical Approach

Abstract

This chapter describes how weaker decision theoretic axioms generate a more plausible description of agents' knowledge and knowledge revision. The results are independent of whether expected utility maximization is assumed to hold. The chapter discusses why the economists' standard model needs to be weakened. Partition information makes too strong implicit assumptions about decision makers' knowledge, such as that the decision maker can anticipate what he would have known in every possible (but not realized) state of the world. However, weakening partition information, while maintaining the standard models of beliefs, is inconsistent. Therefore, a unified approach to modeling the revision of beliefs and knowledge is required. The chapter presents the work in this direction and addresses a problem which arises in the work unified approach to modeling. It is discussed that there is circularity in describing decision makers' preferences over state contingent acts when (implicitly) states are distinguished by the preferences of decision makers at those states. It is necessary to carry out a hierarchical treatment of preferences which addresses this circularity, in the same way that hierarchies of belief and knowledge have addressed circularities which arose in those contexts.