Revision by Conditional Beliefs

Abstract

Both the dynamics of belief change and the process of reasoning by default can be based on the conditional belief set of an agent, represented as a set of “if-then ” rules. In this paper we address the open problem of formalizing the dynamics of revising this conditional belief set by new if-then rules, be they interpreted as new default rules or new revision policies. We start by providing a purely semantic characterization, based on the semantics of conditional rules, which induces logical constraints on any such revision process. We then introduce logical (syntax-independent) and syntax-dependent techniques, and provide a precise characterization of the set of conditionals that hold after the revision. In addition to formalizing the dynamics of revising a default knowledge base, this work also provides some of the necessary formal tools for establishing the truth of nested conditionals, and attacking the problem of learning new defaults.