Unifying default reasoning and belief revision in a modal framework

Abstract

We present a logic for reasoning about belief revision in which the process of revising a knowledge base by some sentence is represented with a conditional connective. The conditional is not primitive however; it is defined in terms of two unary modal operators. We show that our notion of revision is equivalent to that determined by the classic AGM postulates. Furthermore, unlike current models of revision, our approach does not require the Limit Assumption. We also present a model for subjunctive query answering that allows the expression of subjunctive or factual premises, integrity constraints, and notions of entrenchment and plausibility. The modal framework we adopt is sufficiently general to allow the expression of other forms of defeasible reasoning, and facilitates the demonstration of some interesting connections between revision, default reasoning and autoepistemic logic. In particular, we show that the normative conditional for default reasoning (developed in a companion paper) and our subjunctive conditional are identical. Default reasoning can thus be viewed as the revision of a theory of expectations in manner that naturally relates priorities of default rules to the entrenchment of expectations.